{"id":251871,"date":"2026-03-05T14:16:41","date_gmt":"2026-03-05T13:16:41","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=251871"},"modified":"2026-03-05T14:17:16","modified_gmt":"2026-03-05T13:17:16","slug":"triangle-isocele","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/triangle-isocele\/","title":{"rendered":"Tout savoir sur le triangle isoc\u00e8le \ud83d\udd3a"},"content":{"rendered":"\n

Durant ta scolarit\u00e9, tu as appris chaque ann\u00e9e une notion sur le triangle isoc\u00e8le<\/strong>. Aujourd\u2019hui, on te propose un r\u00e9capitulatif <\/strong>de toutes ces informations en un seul et m\u00eame endroit et \u00e7a commence maintenant ! \ud83d\ude0b<\/p>\n\n\n\n

Un triangle est une forme g\u00e9om\u00e9trique. Il est reconnaissable gr\u00e2ce \u00e0 ses trois c\u00f4t\u00e9s. Il existe des dizaines de triangles aux caract\u00e9ristiques diff\u00e9rentes. N\u00e9anmoins, on appelle triangle isoc\u00e8le<\/strong> un triangle qui poss\u00e8de deux c\u00f4t\u00e9s \u00e9gaux<\/strong> (mais pas n\u2019importe lesquels). <\/p>\n\n\n\n

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Un triangle ABC, dont le sommet est A, est isoc\u00e8le si les c\u00f4t\u00e9s adjacents au point A sont \u00e9gaux, soit AB=AC. Ainsi BC repr\u00e9sente la base du triangle.<\/p>\n<\/div>\n\n\n\n

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\"triangle<\/figure>\n<\/div>\n<\/div>\n\n\n
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\ud83d\udca1 \u00c9tymologie<\/p>\n<\/div>\n

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Le mot isoc\u00e8le<\/em> vient du grec iso<\/em> (m\u00eames) et skelos<\/em> (jambes). Autrement dit, isoc\u00e8le<\/em> signifie quelque chose qui a les m\u00eames jambes<\/em>. Or, le dessin d’un triangle isoc\u00e8le fait penser aux deux jambes d’un dessin de bonhomme. Ainsi, le terme isoc\u00e8le repr\u00e9sente deux segments de m\u00eame longueur<\/strong>.<\/p>\n\n <\/div>\n <\/section>\n\n\n

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\u00c0 lire aussi<\/p>\n

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Comment \u00eatre fort en maths ?<\/a><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Les affirmations de base et leurs d\u00e9monstrations<\/h2>\n\n\n\n

\ud83d\udccd Propri\u00e9t\u00e9 g\u00e9n\u00e9rale<\/h3>\n\n\n\n

Un triangle isoc\u00e8le poss\u00e8de deux c\u00f4t\u00e9s et deux angles \u00e9gaux ; en ce sens, un axe de sym\u00e9trie. Cet axe est la m\u00e9diane de la base et la bissectrice de l\u2019angle principal.<\/p>\n\n\n\n

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D\u00e9monstration : <\/p>\n\n\n\n

Voici un triangle isoc\u00e8le.<\/p>\n\n\n\n

AB = AC. BC est la base du triangle. <\/p>\n\n\n\n

La m\u00e9diane (d) part de l\u2019angle primordial et coupe la base BC perpendiculairement. <\/p>\n\n\n\n

(d) est aussi la bissectrice qui s\u00e9pare l\u2019angle A en deux parts \u00e9gales.<\/p>\n\n\n\n

On justifie des segments de m\u00eame longueur par \/\/ ou \/.<\/p>\n<\/div>\n\n\n\n

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\"Illustration<\/figure>\n<\/div>\n<\/div>\n\n\n\n

\ud83d\udccd Propri\u00e9t\u00e9 1 <\/h3>\n\n\n\n

Un triangle isoc\u00e8le<\/strong> poss\u00e8de deux c\u00f4t\u00e9s identiques <\/strong>et deux angles de m\u00eame mesure \u00e0 la base<\/strong>. \u21fe Si un triangle<\/strong> poss\u00e8de deux angles identiques, alors il est isoc\u00e8le\u202f!<\/strong><\/p>\n\n\n\n

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D\u00e9monstration :<\/p>\n\n\n\n

Si AB et AC sont \u00e9gaux,<\/p>\n\n\n\n

Alors l\u2019angle B et l\u2019angle C sont identiques. <\/p>\n\n\n\n

Donc ABC est un triangle isoc\u00e8le. <\/p>\n<\/div>\n\n\n\n

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\"triangle<\/figure>\n<\/div>\n<\/div>\n\n\n\n

\ud83d\udccd Propri\u00e9t\u00e9 2<\/h3>\n\n\n\n

Dans un triangle ABC isoc\u00e8le en A<\/strong>, la m\u00e9diane<\/strong>, la hauteur<\/strong> et la bissectrice<\/strong> sont toutes issues de A ainsi que la m\u00e9diatrice<\/strong> de la base BC. Elles sont donc confondues<\/strong>. <\/p>\n\n\n\n

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\"La
La m\u00e9diane<\/strong> est un segment<\/strong> qui relie le sommet d’un triangle au milieu du c\u00f4t\u00e9 oppos\u00e9<\/strong>.<\/figcaption><\/figure>\n<\/div>\n\n\n\n
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\"La
La hauteur<\/strong> d’un c\u00f4t\u00e9 est la droite qui est perpendiculaire au c\u00f4t\u00e9 et qui passe par le sommet oppos\u00e9.<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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\"La
La bissectrice<\/strong> d’un angle est la droite qui partage un angle en deux angles de m\u00eame mesure<\/strong>.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

Dans un triangle isoc\u00e8le<\/strong>, ces trois segments sont confondus<\/strong>, c’est-\u00e0-dire, qu\u2019ils sont tous les m\u00eames, passant par le m\u00eame sommet et la base<\/strong>.<\/p>\n\n\n

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Louise<\/p>

Mines ParisTech<\/p>

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24\u20ac\/h<\/p> <\/div>\n <\/div>\n

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Nicolas<\/p>

CentraleSup\u00e9lec<\/p>

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17\u20ac\/h<\/p> <\/div>\n <\/div>\n

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Fabien<\/p>

T\u00e9l\u00e9com Paris<\/p>

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Cl\u00e9mence<\/p>

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21\u20ac\/h\/h<\/p> <\/div>\n <\/div>\n

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Bastien<\/p>

Polytechnique<\/p>

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Pierre<\/p>

ESSEC<\/p>

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Simon<\/p>

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Jade<\/p>

Sciences Po Paris<\/p>

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Besoin d’un prof particulier<\/span> de maths ? \u2728<\/span><\/p>\n<\/div>\n

Nos Sherpas sont l\u00e0 pour t’aider \u00e0 progresser et prendre confiance en toi !<\/p>\n<\/div>\n

\n \n JE PRENDS UN COURS OFFERT !\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n\n\n

Les formules de calcul \ud83d\udccf<\/h2>\n\n\n\n

Calculer la hauteur \ud83e\ude9c<\/h3>\n\n\n\n
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Pour calculer la hauteur h<\/em>, on utilise le th\u00e9or\u00e8me de Pythagore<\/a> qui donne la formule :<\/p>\n<\/div>\n\n\n\n

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\"Formule<\/figure>\n<\/div>\n<\/div>\n\n\n\n

D\u00e9monstration : <\/p>\n\n\n\n

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\"triangle<\/figure>\n<\/div><\/div>\n\n\n\n
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\"Calcul
Calcul de la hauteur.<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n

Exemple : <\/p>\n\n\n\n

On a un triangle BAC dont h<\/em> est perpendiculaire \u00e0 BC en un point H. AC = 5 cm et HC = 2 cm.<\/p>\n\n\n\n

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\"triangle<\/figure>\n<\/div><\/div>\n\n\n\n
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\"calcul
h<\/em> mesure environ 4,6 centim\u00e8tres.<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n

Calculer l\u2019aire d\u2019un triangle isoc\u00e8le \u25b2<\/h3>\n\n\n\n

Pour calculer la surface, il suffit de prendre la formule du calcul de l\u2019aire d\u2019un triangle<\/a>. Peu importe les attributs de la forme g\u00e9om\u00e9trique, la formule reste la m\u00eame, \u00e0 savoir : <\/p>\n\n\n

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<\/div>\n
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A = base x h<\/strong> \u00f7 2\u00a0<\/strong><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

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D\u00e9monstration : <\/p>\n\n\n\n

Le triangle BAC est isoc\u00e8le en A. BC = 5 cm et AH <\/p>\n\n\n\n

= 5,5 cm.<\/p>\n\n\n\n

A = base x h \u00f7<\/strong> 2<\/p>\n\n\n\n

A = 5 \u00d7 5,5 \u00f7<\/strong> 2<\/p>\n\n\n\n

A = 13,75<\/p>\n\n\n\n

La surface de A est de 13,75 cm\u00b2.<\/p>\n<\/div>\n\n\n\n

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\"triangle<\/figure>\n<\/div><\/div>\n<\/div>\n\n\n
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\u00c0 lire aussi<\/p>\n

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Comment calculer une aire ?<\/p>\n\n <\/div>\n <\/section>\n\n\n

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<\/div>\n
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On dit souvent que le savoir, c\u2019est le pouvoir. Plus tes connaissances seront nombreuses, plus il sera facile pour toi d\u2019avancer dans ta scolarit\u00e9. Si tu fais partie de ses \u00e9l\u00e8ves qui veulent toujours en savoir plus, n\u2019h\u00e9site pas \u00e0 te tourner vers un de nos professeurs particuliers de math\u00e9matiques<\/a> ! \ud83e\uddd1\u200d\ud83c\udfeb<\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Calculer le p\u00e9rim\u00e8tre d\u2019un triangle isoc\u00e8le \ua554<\/h3>\n\n\n\n

En ce qui concerne sa circonf\u00e9rence, c\u2019est pareil. C\u2019est la m\u00eame formule pour tous les triangles.<\/p>\n\n\n

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<\/div>\n
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P = c \u00d7 c \u00d7 c\u00a0<\/b><\/p>\n

ou\u00a0<\/span><\/p>\n

P = c \u00d7 3<\/b><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

\u00c9tant donn\u00e9 qu\u2019il s\u2019agit ici d\u2019un triangle isoc\u00e8le, deux c\u00f4t\u00e9s ont la m\u00eame longueur x<\/em> et la longueur de la base y<\/em>. Tu peux donc aussi rencontrer la formule : <\/p>\n\n\n

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<\/div>\n
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P = 2x + y <\/b><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

D\u00e9monstration : <\/p>\n\n\n\n

Ici, on a un triangle BAC isoc\u00e8le en A. Puisqu\u2019il est isoc\u00e8le, AC = AB = 5 cm.<\/p>\n\n\n\n

Sa base BC est coup\u00e9e en son centre par la m\u00e9diane. Autrement dit, HC + HB = 2 + 2 = 4 cm. Donc BC = 4 cm. <\/p>\n\n\n\n

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On utilise la formule : P = 2x + y <\/strong><\/p>\n\n\n\n

P = 2 <\/strong>\u00d7 5 + 4 <\/p>\n\n\n\n

P = 10 + 4 <\/p>\n\n\n\n

P = 14<\/p>\n\n\n\n

Donc le p\u00e9rim\u00e8tre est de 14 centim\u00e8tres. <\/p>\n<\/div>\n\n\n\n

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\"dessin<\/figure>\n<\/div><\/div>\n<\/div>\n\n\n
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\u00c0 lire aussi<\/p>\n

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Comment calculer un p\u00e9rim\u00e8tre ?<\/a><\/p>\n\n <\/div>\n <\/section>\n\n\n

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Bastien<\/p>

Polytechnique<\/p>

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Antoine<\/p>

Sciences Po Paris<\/p>

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Cl\u00e9mence<\/p>

HEC Paris<\/p>

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Fanny<\/p>

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Thibault<\/p>

ENS Paris Ulm<\/p>

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Agathe<\/p>

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David<\/p>

EDHEC<\/p>

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Emilie<\/p>

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Coll\u00e9gien en gal\u00e8re ? Ton premier cours est offert ! \ud83c\udf81<\/span><\/p>\n<\/div>\n

Nos profs sont l\u00e0 pour t\u2019aider \u00e0 progresser !<\/p>\n<\/div>\n

\n \n J’EN PROFITE MAINTENANT !\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n\n\n

Les cas particuliers \ud83e\udd13<\/h2>\n\n\n\n

Les triangles rectangles isoc\u00e8les \u25fa<\/h3>\n\n\n\n

Le triangle rectangle isoc\u00e8le est repr\u00e9sent\u00e9 avec les m\u00eames caract\u00e8res que les triangles isoc\u00e8les \u00e9tudi\u00e9s jusqu\u2019\u00e0 pr\u00e9sent. La seule diff\u00e9rence concerne l\u2019angle primordial. <\/p>\n\n\n\n

Prenons le cas de la figure MNO. <\/p>\n\n\n\n

Par d\u00e9finition, un triangle est rectangle lorsqu\u2019un de ces angles \u00e9quivaut \u00e0 90\u00b0, soit un angle droit. Ici, MNO est rectangle en N. <\/p>\n\n\n\n

Il est \u00e9galement isoc\u00e8le, car deux de ses c\u00f4t\u00e9s ont des mesures identiques, MN = NO.<\/p>\n\n\n

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\"Sch\u00e9ma<\/figure>\n<\/div>\n\n
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\ud83d\udca1 Comment calculer l\u2019aire d\u2019un triangle rectangle isoc\u00e8le ?\u00a0<\/span><\/p>\n<\/div>\n

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Exactement de la m\u00eame mani\u00e8re que pour tous les types de formes triangulaires : <\/span>base x h<\/b> \u00f7 2<\/b><\/p>\n\n <\/div>\n <\/section>\n\n\n\n

Exemple : <\/p>\n\n\n\n

Un triangle MNO est rectangle en O et isoc\u00e8le car MO = NO. MO = 6 cm ; MN = 8 cm et h<\/em> = 4 cm.<\/p>\n\n\n\n

Pour calculer l\u2019aire : <\/p>\n\n\n\n

A = base x h \u00f7 2<\/p>\n\n\n\n

A = 8 \u00d7 4 \u00f7 2<\/p>\n\n\n\n

A = 32 \u00f7 2<\/p>\n\n\n\n

A = 16 <\/p>\n\n\n\n

La surface est de 16 cm\u00b2.<\/p>\n\n\n\n

Les triangles \u00e9quilat\u00e9raux \u25b3<\/h3>\n\n\n\n

Pour ce cas, les trois c\u00f4t\u00e9s de la forme g\u00e9om\u00e9trique ont les m\u00eames longueurs. En ce sens, le triangle est forc\u00e9ment isoc\u00e8le en chacun de ses angles. <\/p>\n\n\n\n

Peu importe la longueur des c\u00f4t\u00e9s, un triangle \u00e9quilat\u00e9ral aura toujours ces angles \u00e0 60\u00b0. <\/p>\n\n\n\n

Prenons le cas de la figure MNO.<\/p>\n\n\n\n

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Par d\u00e9finition, un triangle \u00e9quilat\u00e9ral poss\u00e8de ses trois c\u00f4t\u00e9s et ses trois angles \u00e9gaux. <\/p>\n\n\n\n

Donc MN = NO = OM et tous les angles mesurent 60\u00b0.<\/p>\n<\/div>\n\n\n\n

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\"Sch\u00e9ma<\/figure>\n<\/div><\/div>\n<\/div>\n\n\n
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Thibault<\/p>

ENS Paris Ulm<\/p>

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David<\/p>

EDHEC<\/p>

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25\u20ac\/h<\/p> <\/div>\n <\/div>\n

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Cl\u00e9mence<\/p>

HEC Paris<\/p>

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Jade<\/p>

Sciences Po Paris<\/p>

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Victor<\/p>

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Tu veux cartonner au brevet<\/span> ? \u2728<\/p>\n<\/div>\n

Nos profs sont l\u00e0 pour t\u2019aider \u00e0 progresser !<\/p>\n<\/div>\n

\n \n JE PRENDS UN COURS OFFERT !\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/section>\n\n\n\n

 Voici quelques exercices pour t\u2019entra\u00eener \ud83d\udda9<\/h2>\n\n\n\n
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  1. Voici XYZ, d\u00e9finit sa forme avec l\u2019affirmation adapt\u00e9e. <\/li>\n<\/ol>\n\n\n
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    \"forme<\/figure>\n<\/div>\n\n\n

    2. Calcule h<\/em> toujours avec XYZ.<\/p>\n\n\n

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    \"triangle<\/figure>\n<\/div>\n\n\n

    3. Trouve l\u2019aire de XYZ avec les r\u00e9sultats obtenus. <\/p>\n\n\n\n

    Corrections des exercices ! <\/h3>\n\n\n\n
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    1. Dans ce cas, on peut identifier la propri\u00e9t\u00e9 1.<\/li>\n<\/ol>\n\n\n\n

      Un <\/em>triangle isoc\u00e8le<\/em><\/strong> poss\u00e8de<\/em> deux c\u00f4t\u00e9s \u00e9gaux <\/em><\/strong>et <\/em>deux angles de m\u00eame mesure \u00e0 la base<\/em><\/strong>. \u21fe Si un <\/em>triangle<\/em><\/strong> poss\u00e8de deux angles identiques, alors il est <\/em>isoc\u00e8le\u202f!<\/em><\/strong><\/p>\n\n\n\n

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      1. On utilise le th\u00e9or\u00e8me de Pythagore. <\/li>\n<\/ol>\n\n\n\n

        Le r\u00e9sultat obtenu doit \u00eatre d\u2019environ 5,4 cm.<\/p>\n\n\n\n

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        1. On utilise la formule : A = base x h \u00f7 2.<\/li>\n<\/ol>\n\n\n\n

          La surface est de 13,5 cm\u00b2.<\/p>\n\n\n

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          \n \n \n \n \"reverse\n <\/picture>\n
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          Nul en maths ? Essaye le retro-engineering !<\/p>\n<\/div>\n