4-5 Isosceles &amp; Equilateral Triangles

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4-5 Isosceles &amp; Equilateral Triangles. Objectives: To use and apply properties of isosceles and equilateral triangles. Solve It!. Isosceles vs Equilateral. What is an isosceles triangle? What is an equilateral triangle? Label the following on the diagram below: Legs Base Base angle

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### 4-5 Isosceles & Equilateral Triangles

Objectives: To use and apply properties of isosceles and equilateral triangles

Isosceles vs Equilateral
• What is an isosceles triangle?
• What is an equilateral triangle?
• Label the following on the diagram below:
• Legs
• Base
• Base angle
• Vertex angle
Isosceles Triangle Theorem
• If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isosceles Theorem
• If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Theorem 4-5
• If a line bisects the vertex angle of an isosceles triangle, then the line is also perpendicular bisector of the base.
Corollary (4-3)
• If a triangle is equilateral, then the triangle is equiangular
Corollary (4-4)
• If a triangle is equiangular, then the triangle is equilateral
Example 1
• Given: G, H, and L are congruent
• Is GK = HK ?
• Is HL = KJ ?

G

H

K

L

J

Example Two
• What is the value of x?

7x – 10

3x + 6

Example Three
• In the diagram, PLN = LNS. What is the measure of S in the figure below?

L

P

50º

S

N

Homework Section 4-5
• Page 254 #6-22 evens, 28