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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q10 (page 186)

For the following figure, $∠ K A P$ is a right angle and $\bar{A M}$ is a median then complete the statement
If $m ∠ K = 40$ then $m ∠ K A M =__$ .

Short Answer

Expert verified

The statement is “if $m ∠ K = 40$ , then $m ∠ K A M = 40$ .

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

For the right-angle triangle, the median is equal to one-half of the hypotenuse.

Here the angle KAP is a right-angle triangle.

03

Step 3. Step description.

Now, simplify the figure as follows:

$\begin{matrix} A M = \frac{K P}{2} \\ A M = \frac{2 M K}{2} \\ A M = M K \end{matrix}$

Now, opposite angles of equal sides must be equal for triangle MKA.

$\begin{array}{l} m ∠ K = m ∠ K A M \\ m ∠ K A M = 40 \end{array}$

Thus, the statement is $m ∠ K A M = 40$ .

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Most popular questions from this chapter

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

$S O = \frac{1}{2} S C; K O = \frac{1}{2} K A$

What values must x and y have to make the quadrilateral a parallelogram?

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

See all solutions

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