Unit 5 test: Congruent Triangles

Given $\triangle ABC \cong \triangle RST$, which angle is congruent to $\angle C$?

Given $\triangle KLM \cong \triangle XYZ$, $KL = 3x + 2$ and $XY = 5x - 8$. Find $KL$.

$\triangle ABC$ has vertex $A(2, 3)$. It is reflected across the $x$-axis to form the congruent triangle $\triangle A'B'C'$. What are the coordinates of $A'$?

Which shortcut proves the triangles congruent?

In $\triangle PQR$ and $\triangle STU$, $\overline{PQ} \cong \overline{ST}$, $\overline{QR} \cong \overline{TU}$ and $\angle R \cong \angle U$. What can you conclude?

$\triangle ABC$ has $AB = 5$, $BC = 12$ and $m\angle B = 90^\circ$. $\triangle DEF$ has $DE = 5$, $EF = 12$ and $m\angle E = 90^\circ$. The triangles are congruent by SAS. Find $DF$.

In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$, $\angle B \cong \angle E$ and $\overline{BC} \cong \overline{EF}$. Which shortcut proves the triangles congruent?

$\triangle PQR \cong \triangle STU$ by ASA. $m\angle P = 47^\circ$ and $m\angle U = 58^\circ$. Find $m\angle Q$ in degrees.

Given: $\overline{AB} \parallel \overline{CD}$, and $E$ is the midpoint of $\overline{AD}$. Prove: $\triangle ABE \cong \triangle DCE$.

What is the missing reason in step 2?

$\triangle JKL$ and $\triangle MNP$ are right triangles with right angles at $K$ and $N$. $\overline{JL} \cong \overline{MP}$ and $\overline{KL} \cong \overline{NP}$. Which shortcut proves $\triangle JKL \cong \triangle MNP$?

$\triangle ABC \cong \triangle DEF$ by HL, with right angles at $B$ and $E$. The hypotenuse $\overline{AC}$ has length $10$ and leg $\overline{AB}$ has length $6$. Find $EF$.

In quadrilateral $ABCD$, $\overline{AB} \parallel \overline{DC}$ and $\overline{AB} \cong \overline{DC}$, and diagonal $\overline{AC}$ is drawn, so $\triangle BAC \cong \triangle DCA$ by SAS. If $BC = 3y - 4$ and $DA = y + 10$, find $BC$.

The vertex angle of an isosceles triangle measures $36^\circ$. What is the measure of each base angle, in degrees?

In $\triangle ABC$, $\overline{AB} \cong \overline{AC}$, $m\angle B = (5x - 7)^\circ$ and $m\angle C = (3x + 17)^\circ$. Find $m\angle A$ in degrees.

An equilateral triangle has sides of length $4x + 3$ and $7x - 9$. Find its perimeter.