Chapter 4: Q8. (page 136)

For the following figure, is the statement “ $\bar{M K} ≅ \bar{N K}$ if and only if $∠ 3 ≅ ∠ 4$ ” is true or false.

Short Answer

Expert verified

The statement is a true statement.

Step by step solution

Step 1. Check the figure.

Consider the figure.

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.

Step 3. Step description.

From the figure, consider the triangle $Δ K M N$ and $\bar{M K} ≅ \bar{N K}$ .

Since from isosceles triangle theorem if two sides of a triangle are congruent, then the angles opposite those sides are congruent thus $∠ 3 ≅ ∠ 4$ .

Therefore, $∠ 3 ≅ ∠ 4$ .

Prove the converse as follows:

In $Δ K M N$ , $∠ 3 ≅ ∠ 4$ that is the base angles are congruent.

Thus $Δ K M N$ is an isosceles triangle.

Since in an isosceles triangle, sides opposite to these congruent angles will also be congruent thus $\bar{M K} ≅ \bar{N K}$

Therefore, the congruent sides are $\bar{M K} ≅ \bar{N K}$ .

Thus, the statement is true statement.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the following figure, is the statement “ $\bar{M K} ≅ \bar{N K}$ if and only if $∠ 3 ≅ ∠ 4$ ” is true or false.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of isosceles triangle.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

For the following figure, is the statement “ MK¯≅NK¯if and only if ∠3≅∠4” is true or false.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of isosceles triangle.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

For the following figure, is the statement “ $\bar{M K} ≅ \bar{N K}$ if and only if $∠ 3 ≅ ∠ 4$ ” is true or false.