4.7 Use Isosceles and Equilateral Triangles

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Presentation transcript:

4.7 Use Isosceles and Equilateral Triangles

Isosceles Triangle A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles) vertex Leg Leg base angle base angle Base

Isosceles Triangle Theorem (Base Angles Theorem) If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent B C A B C A

Use the Isosceles Triangle Theorem

Converse of the Isosceles Triangle Theorem (Converse of the Base Angles Theorem) If two angles of a triangle are congruent, then the sides opposite them are congruent B C A B C A

Example Use the diagram. Copy and complete the statement. Tell what theorem you used. a.If AE DE, then <___ <___ b.If AB EB, then <___ <___ c.If <D <CED, then ___ ___. E A B C D

Corollaries Corollarary to the Base Angles Theorem If a triangle is equilateral, then it is equiangular Corollarary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is equilateral

Example Find the value of x. x 12 72° x

Example Find the unknown measure. x 15 72° x 42° 42°

Example Find the value of x. (2x + 9)° 12x° 72° (4x – 7)°

Example Find the value of x. 40° 80° 2x° (4x – 6)°

Example Find the unknown measure. x 60° 60° 20 ?

Example Find the value of x. 5 3x° 5x + 5 16 5 5 35

Example Find the perimeter of the triangle. (7x - 13) in (x + 29) in (8x - 15) m (4x + 3) m (3x + 5) in (5x + 8) m