Lesson 4 Congruent Triangles Solidify Understanding

Ready

Given the figures with congruent angles and sides marked in each sketch, first list the parts of the figures that are corresponding and congruent (for example, in problem 1, $∠ C ≅ ∠ R$ ). Then determine if a reflection occurred as part of the sequence of transformations that was used to create the image.

1.

Congruencies:

$∠ C ≅ ∠ R$

Reflected? Yes or No

2.

Congruencies:

Reflected? Yes or No

Set

Use the congruence markings to determine whether the triangles are congruent, similar, or neither. State the triangle congruence criterion connected to the pair of triangles that are congruent or similar.

3.

4.

5.

6.

7.

8.

9.

Provide a sequence of transformations that can be used to justify that triangle $V W Z$ is congruent to triangle $L N M$ . Explain how the congruent features indicated on the triangles and the transformations prove that the triangles are congruent.

10.

Describe a sequence of transformations and a triangle congruence criterion to justify that triangle $E F D$ is congruent to triangle $Y X Z$ .

Use the given congruence statements to draw and label two triangles so that the corresponding parts are congruent.

11.

$△ A B C ≅ △ P Q R$

12.

$△ X Y Z ≅ △ K L M$

Go

Solve each equation for $t$ .

13.

$\frac{3 t - 4}{5} = 5$

14.

$10 - t = 4 t + 12 - 3 t$

15.

$P = 5 t - d$

16.

$x y - t = 13 t + w$

Use a compass and a straightedge to construct each figure.

17.

Construct an equilateral triangle with the given segment as one of its sides.

18.

Construct a rhombus with $\overset{―}{A B}$ as one side of the rhombus and angle $A$ as one of the angles of the rhombus.