# Congruent Parts, Part 1

10 questions

# Congruent Parts, Part 1

##### Problem 1

1) When rectangle $ABCD$ is reflected across line $EF$, the image is $DCBA$. How do you know that segment $AB$ is congruent to segment $DC$?

A rectangle has 2 pairs of parallel sides.

Any 2 sides of a rectangle are congruent.

Congruent parts of congruent figures are corresponding.

Corresponding parts of congruent figures are congruent.

##### Problem 2

2) Triangle $FGH$ is the image of isosceles triangle $FEH$ after a reflection across line $HF$. Select $\textbf{all}$ the statements that are a result of corresponding parts of congruent triangles being congruent. Write each corresponding letter in the answer box and separate letters with commas.

a) $EFGH$ is a rectangle. $\quad\quad$ b) $EFGH$ has 4 congruent sides. $\quad\quad$ c) Diagonal $FH$ bisects angles $EFG$ and $EHG$.

d) Diagonal $FH$ is perpendicular to side $FE$. $\quad\quad$ e) Angle $FEH$ is congruent to angle $FGH$.

##### Problem 3

3) Reflect right triangle $ABC$ across line $BC$.

4) Classify triangle $ACA'$ according to its side lengths.

5) Explain how you know.

##### Problem 4

6) Triangles $FAD$ and $DCE$ are translations of triangle $ABC$.

Select $\textbf{all}$ the statements that $\textit{must}$ be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Points $B$, $A$, and $F$ are collinear. $\quad\quad$ b) The measure of angle $BCA$ is the same as the measure of angle $CED$.

c) Line $AD$ is parallel to line $BC$. $\quad\quad$ d) The measure of angle $CED$ is the same as the measure of angle $FAD$.

e) The measure of angle $DAC$ is the same as the measure of angle $BCA$.

f) Triangle $ADC$ is a reflection of triangle $FAD$.

##### Problem 5

Triangle $ABC$ is congruent to triangles $BAD$ and $CEA$.

7) Explain why points $D$, $A$, and $E$ are collinear.

8) Explain why line $DE$ is parallel to line $BC$.

##### Problem 6

9) Identify a figure that is the result of a rigid transformation of quadrilateral $ABCD$.

10) Describe a rigid transformation that would take $ABCD$ to that figure.