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Chapter 4: Q8. (page 136)

For the following figure, is the statement 鈥� MK炉鈮�NK炉if and only if 鈭�3鈮�鈭�4鈥� is true or false.

Short Answer

Expert verified

The statement is a true statement.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Apply the concept of isosceles triangle.

Property of isosceles triangle states that in an isosceles triangle, sides opposite to equal opposite angles are also congruent.

03

Step 3. Step description.

From the figure, consider the triangle 螖KMNand MK炉鈮�NK炉.

Since from isosceles triangle theorem if two sides of a triangle are congruent, then the angles opposite those sides are congruent thus 鈭�3鈮�鈭�4.

Therefore, 鈭�3鈮�鈭�4.

Prove the converse as follows:

In 螖KMN, 鈭�3鈮�鈭�4that is the base angles are congruent.

Thus螖KMN is an isosceles triangle.

Since in an isosceles triangle, sides opposite to these congruent angles will also be congruent thusMK炉鈮�NK炉

Therefore, the congruent sides are MK炉鈮�NK炉.

Thus, the statement is true statement.

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