CK-12 Geometry-Concepts

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

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.

Interactive Practice