4 7 Use Isosceles and Equilateral Triangles Hubarth

4. 7 Use Isosceles and Equilateral Triangles Hubarth Geometry

The congruent sides of an isosceles triangle are called legs. The other side is called the base. The two angles at the base of the triangle are called the base angles. A leg vertex angle leg base angles B Theorem 4. 3 Base Angles Theorem base C

Ex 1. Use the Base Angle Theorem M 52 L Solution N

Theorem 4. 4 Converse of the Base Angle Theorem A B C

Ex 2. Use the Converse of the Base Angles Theorem Find the value of x. F 12 D Solution X+3 E

Corollaries Corollary to the Base Angles Theorem B Corollary to the Converse of Base Angles Theorem A C

Ex 3. Find the Side Length of an Equiangular Triangle Find the length of each side of the equiangular triangle. 3 x 2 x+10 Solution Because the triangle is equiangular, it is also equilateral. So, 3 x=2 x+10 x=10 3(10)=30 Each side of the triangle is 30

EX 3 Use Isosceles and Equilateral Triangles Find the values of x and y in the diagram. STEP 1 STEP 2 LN = LM Definition of congruent segments 4=x+1 Substitute 4 for LN and x + 1 for LM. 3=x Subtract 1 from each side.

Practice Find the value of y. y=50 1. y=9 2. y 50 3. 16 9 y y+4=16 -4 -4 y=12 Y+4 5. Find the values of x and y in the diagram. B 4. 58 y° = 120° x° = 60° 6 x+4 A C