Yippee for them, but what do we know about their base angles How do we know those are equal, too We reach into our geometer's toolbox and take out the Isosceles Triangle Theorem. The angle bisector of the triangle is perpendicular to the side with different length. Chapter 10 Isosceles Triangles Chapter 11 Inequalities Chapter 12 Mid-point and Its Converse Including Intercept Theorem Chapter 13 Pythagoras. Definition Properties Isosceles triangle theorem Converse Converse proof Isosceles triangle Isosceles triangles have equal legs (that's what the word 'isosceles' means). 1: Draw C D, the angle bisector of A C B (Figure 3.5. 1 is sometimes stated in the following way: 'The base angles of an isosceles triangle are equal,' Proof of Theorem 3.5. The angle bisector divides the unequal angle into equal half. In A B C if A C B C then side A B is called the base of the triangle and A and B are called the base angles. Note: In isosceles triangle the two sides are equal and the two angles corresponding to the sides are equal. $\therefore $ proved the converse Isosceles Triangle Theorem. The proof is very quick: if we trace the bisector of C that meets the opposite side AB in a point P, we get that the angles ACP and BCP are congruent. Since corresponding part of congruent triangles are congruent, so the two sides of the triangle will be equal, which is The converse of the Isosceles Triangle Theorem states that if two angles A and B of a triangle ABC are congruent, then the two sides BC and AC opposite to these angles are congruent. So by the$AAS$ property of triangle the two triangle $\vartriangle ABD$ and $\vartriangle ACD$ are congruent. Consider isosceles triangle \triangle ABC ABC with ABAC, AB AC, and suppose the internal bisector of \angle BAC BAC intersects BC BC at D. Search Result for Isosceles triangle theorem and its converse. Conversely, if the base angles of a triangle are equal, then the triangle is isosceles. Free Online ISOSCELES-TRIANGLE-THEOREM-AND-ITS-CONVERSE Practice
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