Similarity and AA: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Triangle $ABC$ has angles
$\begin{aligned}A&=32^\circ\\B&=73^\circ.\end{aligned}$
Triangle $DEF$ has angles
$\begin{aligned}D&=75^\circ\\E&=32^\circ.\end{aligned}$
Which statement follows?

Answer choices for question 1 A $\triangle ABC\sim\triangle DEF$ B $\triangle ABC\sim\triangle EFD$ C $\triangle ABC\sim\triangle FDE$ D The triangles cannot be similar
2

It is given that $\triangle RST\sim\triangle KLM$ . If
$\begin{aligned}RS&=16\\KL&=12\\LM&=18\end{aligned}$
, find $ST$ .

Answer choices for question 2 A $24$ B $13.5$ C $22$ D $30$
3

Given $\triangle ABC\sim\triangle XYZ$ , suppose
$\begin{aligned}AB&=6\\XY&=9\\AC&=2t+1.\end{aligned}$
If $XZ=19.5$ , find $t$ .

Answer choices for question 3 A $4$ B $9$ C $6$ D $12$
4

In triangle $ABC$ , $D$ lies between $A$ and $B$ , $E$ lies between $A$ and $C$ , and $DE\parallel BC$ . Which angle equals $\angle ADE$ by corresponding angles?

Answer choices for question 4 A $\angle ACB$ B $\angle BAC$ C $\angle DEA$ D $\angle ABC$
5

Points $A,O,C$ and $B,O,D$ are each collinear in the stated orders. Which angle is vertical to $\angle AOB$ ?

Answer choices for question 5 A $\angle COD$ B $\angle BOC$ C $\angle AOD$ D $\angle CDO$
6

In the crossing configuration, $A,O,C$ and $B,O,D$ are collinear in order. In addition, $AB\parallel CD$ . What is a valid second angle match for proving $\triangle AOB\sim\triangle COD$ ?

Answer choices for question 6 A $\angle BAO\cong\angle CDO$ B $\angle ABO\cong\angle DCO$ C $\angle BAO\cong\angle DCO$ D $\angle AOB\cong\angle CDO$
7

Angles $A$ and $B$ of triangle $ABC$ match angles $P$ and $Q$ of triangle $PQR$ . Which dilation factor makes the included side $AB$ match $PQ$ ?

Answer choices for question 7 A $\frac{AB}{PQ}$ B $\frac{PQ}{AB}$ C $PQ-AB$ D $\frac{PR}{BC}$
8

Equal angle pairs are $A$ to $P$ and $B$ to $Q$ . A dilation has made $AC$ equal to $PR$ . Without finding another angle, which earlier congruence criterion applies to the dilated triangle and $PQR$ ?

Answer choices for question 8 A ASA congruence B SSS congruence C SAS congruence D AAS congruence
9

Two triangles are known similar. One pair of corresponding angles has measures $(3x+8)^\circ$ and $86^\circ$ . Find $x$ .

Answer choices for question 9 A $78$ B $\frac{94}{3}$ C $43$ D $26$
10

It is given that $\triangle ABC\sim\triangle XYZ$ . Which equation consistently compares second-triangle lengths with first-triangle lengths?

Answer choices for question 10 A $\frac{XY}{AB}=\frac{BC}{YZ}$ B $\frac{XY}{AB}=\frac{YZ}{BC}$ C $\frac{XY}{BC}=\frac{YZ}{AB}$ D $\frac{XZ}{AB}=\frac{XY}{AC}$
11

Two similar triangles have scale factor 1, but one is turned and reflected. Which statement is correct?

Answer choices for question 11 A They cease to be similar when reflected B They are congruent only after every vertex is already aligned C They are congruent because a rigid-motion match is possible D Their corresponding angles may differ
12

Given $\triangle ABC\sim\triangle RQP$ , suppose
$\begin{aligned}AB&=11\\RQ&=22\\AC&=9.\end{aligned}$
Find $RP$ .

Answer choices for question 12 A $18$ B $4.5$ C $20$ D $27$