Chapter 11.2, Problem 26HP

a.

To determine

whether the given statement is true or false

Answer to Problem 26HP

True

Explanation of Solution

Given information:Triangles EFG and KLM are congruent. So, their perimeters are equal.

As $\Delta EFG\cong \Delta KLM$ ,

  $EF=KL,FG=LM,EG=KM$ (corresponding sides of congruent triangles are equal)

Perimeter of $\Delta EFG$ = sum of all sides of $\Delta EFG$

  $\begin{array}{l}=EF+FG+EG\\ =KL+LM+KM\end{array}$

= perimeter of $\Delta KLM$

So, the given statement is true.

b.

To determine

whether the given statement is True or False

Answer to Problem 26HP

True

Explanation of Solution

Given information: Triangles WXY and HJK are congruent. So, their areas are equal.

  $\Delta EFG\cong \Delta KLM$

As congruent figures have equal area, $\Delta EFG,\Delta KLM$ have equal areas.

So, the given statement is true.

c.

To determine

To find: whether the given statement is true or false.

Answer to Problem 26HP

False

Explanation of Solution

Given information: The perimeter of triangle ABC is 24 millimeters and perimeter of triangle RST is 24 millimeters. So, triangles are ABC and RST are congruent.

Let sides of triangle ABC be $AB=8mm,BC=9mm,AC=7mm$

So, perimeter of triangle ABC = $AB+BC+AC=8+9+7=24mm$

Let sides of triangle RST be $RS=6mm,ST=10mm,RT=8mm$

Perimeter of triangle RST = $RS+ST+RT=6+10+8=24mm$

So,

Perimeter of triangle ABC = perimeter of triangle RST

But corresponding sides of triangle ABC and triangle RST are not equal, so these triangles are not congruent.

So, the given statement is false.