5 7 Isosceles and Equilateral Triangles Proof Geometry

5 -7 Isosceles and Equilateral Triangles Proof Geometry

Classifying Triangles by Sides . 02 =3 cm AB 47 3. BC = 3. 55 cm cm C = . 15 =3 B B = A C 7 4 3. cm A A AC cm Scalene: A triangle in which all 3 sides are different lengths. A B C BC = 5. 16 cm Isosceles: A triangle in which at least 2 sides are equal. G GI =3 Equilateral: A triangle in which all 3 sides are equal. . 70 H cm GH = 3. 70 cm HI = 3. 70 cm I

Classifying Triangles by Angles Acute: A triangle in which all 3 angles are less than 90˚. G 76° 57° H Obtuse: A triangle in which one and only one angle is greater than 90˚& less than 180˚ B 47° A 44° 28° 108° C I

Classifying Triangles by Angles Right: A triangle in which one and only one angle is 90˚ Equiangular: A triangle in which all 3 angles are the same measure.

Isosceles Triangle ØAn Isosceles Triangle has two congruent sides called the legs. ØThe angle formed by the two legs is the vertex angle ØThe third side is called the base. ØThe two angles adjacent to the base are called the base angles.

The Isosceles Triangle Theorem

Converse of the Isosceles Triangle Theorem

• Every equilateral triangle is equiangular

• Every equiangular triangle is equilateral

Challenge Problem:

Homework Pg. 157: #2, 3, 6, 7, 10, 11, 16