5-7 Isosceles and Equilateral Triangles

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Presentation transcript:

5-7 Isosceles and Equilateral Triangles Proof Geometry

Classifying Triangles by Sides Scalene: A triangle in which all 3 sides are different lengths. BC = 5.16 cm B C A BC = 3.55 cm A B C AB = 3.47 cm AC = 3.47 cm AB = 3.02 cm AC = 3.15 cm Isosceles: A triangle in which at least 2 sides are equal. HI = 3.70 cm G H I Equilateral: A triangle in which all 3 sides are equal. GI = 3.70 cm GH = 3.70 cm

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

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

The Isosceles Triangle Theorem

Converse of the Isosceles Triangle Theorem

Corollary based on Isosc. ∆ Thm. Every equilateral triangle is equiangular

Corollary based on Converse of Isosc. ∆ Thm. Every equiangular triangle is equilateral

Challenge Problem:

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