Chapter 5: Q6 (page 195)

Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
M is the midpoint of hypotenuse $A M$ and $m ∠ A C M$

Short Answer

Expert verified

$A M = 17, m ∠ A C M = 67$

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Consider the triangle $Δ A C B$ .

Now, $\bar{A B}$ is the hypotenuse of the right triangle $Δ A C B$ and M is its midpoint.

So, by the theorem, the midpoint M of the hypotenuse $\bar{A B}$ of a right triangle $Δ A C B$ is equidistant from the three vertices.

Thus, $B M = A M = C M = 17$

Step 3. Step description.

Now, consider the triangle $Δ M C B$ , here $\bar{B M} ≅ \bar{A M}$ , so by theorem , the angles $∠ M C B$ and $∠ M B C$ are congruent.

That is, $m ∠ M C B = m ∠ M B C = 23$ .

As $m ∠ A C B = 90$ , so

$\begin{matrix} m ∠ A C B = 90 \\ m ∠ A C M + m ∠ M C B = 90 \\ m ∠ A C M + 23 = 90 \end{matrix}$

$\begin{matrix} m ∠ A C M = 90 - 23 \\ m ∠ A C M = 67 \end{matrix}$

Therefore, $A M = 17, m ∠ A C M = 67$ .

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Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
M is the midpoint of hypotenuse $A M$ and $m ∠ A C M$

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

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Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.M is the midpoint of hypotenuse AMandm∠ACM

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Calculus

Mechanics Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
M is the midpoint of hypotenuse $A M$ and $m ∠ A C M$