# Congruent Triangles, Part 2

# Congruent Triangles, Part 2

##### Problem 1

Match each statement using only the information shown in the images of pairs of congruent triangles. Write the number of the corresponding image in the answer box.

1) In the 2 triangles there are 3 pairs of congruent sides.

2) The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

3) The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

##### Problem 2

4) Sketch the unique triangles that can be made with angle measures $40\degree$ and $100\degree$ and side length 3.

5) How do you know you have sketched all possibilities?

##### Problem 3

6) What is the least amount of information that you need to construct a triangle congruent to this one?

##### Problem 4

7) Triangle $ABC$ is congruent to triangle $EDF$. So, Mai knows that there is a sequence of rigid motions that takes $ABC$ to $EDF$.

Select **all** true statements after the transformations. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle $A$ coincides with angle $E$. $\quad\quad$ b) Angle $B$ coincides with angle $F$. $\quad\quad$ c) Segment $AB$ coincides with segment $EF$. $\quad\quad$ d) Segment $BC$ coincides with segment $DF$. $\quad\quad$ e) Segment $AC$ coincides with segment $ED$.

##### Problem 5

A rotation by angle $ACE$ using point $C$ as the center takes triangle $CBA$ onto triangle $CDE$.

8) Explain why the image of segment $CB$ lines up with ray $CD$.

9) Explain why the image of $B$ coincides with $D$.

10) Is triangle $ABC$ congruent to triangle $EDC$?

11) Explain your reasoning.

##### Problem 6

Line $EF$ is a line of symmetry for figure $ABECDF$. Clare says that $ABEF$ is congruent to $CDFE$ because sides $AB$ and $CD$ are corresponding.

12) Why is Clare's congruence statement incorrect?

13) Write a correct congruence statement for the quadrilaterals.

##### Problem 7

14) Triangle $HEF$ is the image of triangle $HGF$ after a reflection across line $FH$.

Select **all** statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle $FGH$ is congruent to triangle $FEH$. $\quad\quad$ b) Triangle $EFH$ is congruent to triangle $GFH$. $\quad\quad$ c) Angle $HFE$ is congruent to angle $FHG$. $\quad\quad$ d) Angle $EFG$ is congruent to angle $EHG$. $\quad\quad$ e) Segment $EH$ is congruent to segment $FG$. $\quad\quad$ f) Segment $GH$ is congruent to segment $HE$.

##### Problem 8

15) When rectangle $ABCD$ is reflected across line $EF$, the image is $BADC$. How do you know that segment $AD$ is congruent to segment $BC$?

##### Problem 9

16) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.