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Geometry
4.7 Isosceles and Equilateral Triangles
Name: _______________________
A triangle is isosceles if it has at least ______ congruent sides.
When an isosceles triangle has EXACTLY two congruent sides, the two sides are called the
___________
Vertex Angle- The angle formed by the legs
Base- The third remaining side (not the legs)
Base Angles- The angles _______________________ to the base
Base Angles Theorem- If two sides of a triangle are congruent, then the angles opposite them
(the base angles) are congruent.
Converse of the Base Angles Theorem- If two angles of a triangle are congruent, then the
sides opposite them (the legs) are congruent.
Examples:
1. If ̅̅̅̅
𝐻𝐺 ≅ ̅̅̅̅
𝐻𝐾 , then ∠ ___________ ≅ ∠ ___________
2. If ∠ 𝐾𝐻𝐽 ≅ ∠ 𝐾𝐽𝐻, then ________ ≅ ________
Practice Problems:
1. Find 𝑚∠𝐹.
2. Find the value of x.
3. Find the value of y and the 𝑚∠𝑃.
Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is ____________________
Corollary to the Converse of the Base Angles Theorem
If a triangle is equiangular, then it is _____________________
4. Find the values of x and y.
5. Find the values of x and y.
6. Find the value of x.
.
7. Find the value of y and 𝑁𝑃.
8. Find the value of t.
9. Find the value of x.
10. Is it possible to find the values of x and y? If so, find them.