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Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q2 (page 121)

Given: $\overset{炉}{FC}$ and $\overset{炉}{SH}$ bisect each other at $A;$ localid="1638250328146" $FC = SH$ .
Prove: $SA = AC$ .

Short Answer

Expert verified

It is proved that $\overset{炉}{A C} = \overset{炉}{S A}$ .

Step by step solution

01

Step 1. Consider the diagram.

Here, $\overset{炉}{F C}$ , $\overset{炉}{S H}$ bisect each other $A$ and $\overset{炉}{F C} = \overset{炉}{S H}$

02

Step 2. State the proof.

As $\overset{炉}{F C}$ , $\overset{炉}{S H}$ bisect each other $A$ ,

$\overset{炉}{A C} = \frac{1}{2} (\overset{炉}{F C})$ and $\overset{炉}{S A} = \frac{1}{2} (\overset{炉}{S H})$

Also,

$\overset{炉}{F C} = \overset{炉}{S H}$ (Given)

Multiply both sides by $\frac{1}{2}$ .

$\begin{matrix} \frac{1}{2} (\overset{炉}{F C}) = \frac{1}{2} (\overset{炉}{S H}) \\ \overset{炉}{A C} = \overset{炉}{S A} \end{matrix}$

03

Step 3. State the conclusion.

Therefore, $\overset{炉}{A C} = \overset{炉}{S A}$ (proved).

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Most popular questions from this chapter

Suppose that $螖 F I N 鈮� 螖 W E B,$ then is the following statement is the correct way to say?

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

Plot the given points on graph paper. Draw $螖 ABC$ and $\overset{炉}{DE}$ . Find two locations of point $F$ such that $螖 ABC 鈮� 螖 DEF$ .

$A (鈭� 1, 0)$ $B (鈭� 5, 4)$ $C (鈭� 6, 1)$ $D (1, 0)$ $E (5, 4)$ .

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

Given: $鈭� 4 鈮� 鈭� 7; 鈭� 1 鈮� 鈭� 3$

Prove: $螖 ABC$ is isosceles.

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