CK-12 Geometry Concepts

http://www.ck12.org Chapter 4. Triangles and Congruence

2. Fill in the proof:

Given: Equilateral 4 RSTwith

RT∼=ST∼=RS

Prove: 4 RSTis equiangular

TABLE4.19:

Statement Reason

1. 
   
   
   
   1. Given
   
   
   
   


2. 
   
   
   
   2. Base Angles Theorem
   
   
   
   


3. 
   
   
   
   3. Base Angles Theorem
   
   
   
   


4. 
   
   
   
   4. Transitive PoC
   
   
   
   


5. 4 RSTis equiangular 5.


6. True or false: All equilateral triangles are isosceles triangles.

Answers:

1. The markings show that all angles are congruent. Since all three angles must add up to 180◦this means that each
   angle must equal 60◦. Write and solve an equation:

8 y+ 4 = 60

8 y= 56

y= 7

2.

TABLE4.20:

Statement Reason

1.RT∼=ST∼=RS 1. Given

2.^6 R∼=^6 S 2. Base Angles Theorem
3.^6 T∼=^6 R 3. Base Angles Theorem
4.^6 T∼=^6 S 4. Transitive PoC
5. 4 RSTis equiangular 5. Definition of equiangular.
3. This statement is true. The definition of an isosceles triangle is a triangle with at least two congruent sides. Since
all equilateral triangles have three congruent sides, they fit the definition of an isosceles triangle.

Practice

The following triangles are equilateral triangles. Solve for the unknown variables.

1.

2.

3.

4.

5.

6.