Level 2 · Intermediate ← Back to lesson

SAS and ASA Congruence: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

For an SAS match, corresponding sides have lengths $4x-3$ cm and $2x+9$ cm. The other side pair and included angles already match. What value of $x$ completes the match?

Answer choices for question 1 A $3$ B $12$ C $6$ D $-6$
2

Two triangles already have matching included sides and one endpoint-angle pair. Their remaining endpoint angles measure $(3x+5)^\circ$ and $74^\circ$ . What $x$ completes ASA?

Answer choices for question 2 A $23$ B $\dfrac{79}{3}$ C $69$ D $79$
3

The given matching parts are:
$\begin{aligned} DE&=VT \\ DF&=VU \\ \angle EDF&\cong\angle TVU \end{aligned}$
Which ordered statement follows by SAS?

Answer choices for question 3 A $\triangle DEF\cong\triangle VUT$ B $\triangle DEF\cong\triangle TVU$ C $\triangle DEF\cong\triangle UTV$ D $\triangle DEF\cong\triangle VTU$
4

An ASA construction has a $14$ cm base and endpoint angles $52^\circ$ and $79^\circ$ . What is the third angle?

Answer choices for question 4 A $131^\circ$ B $49^\circ$ C $27^\circ$ D $59^\circ$
5

A report lists these matching parts:
$\begin{aligned} AB&=DE \\ AC&=DF \\ \angle B&\cong\angle E \end{aligned}$
What would be needed to use SAS directly with those two side pairs?

Answer choices for question 5 A $\angle A\cong\angle D$ B $\angle C\cong\angle F$ C $AB=EF$ D No additional angle information
6

After aligning two equal bases, the third vertices lie on opposite sides of the base line. Which rigid motion keeps both base endpoints fixed and changes the side of the third vertex?

Answer choices for question 6 A A nonzero translation along the base B A quarter-turn about the base midpoint C Reflection across the base line D A stretch perpendicular to the base
7

In the ASA justification, why can the aligned angle rays not give two different third vertices in the same half-plane?

Answer choices for question 7 A Every triangle has three equal sides B The two distinct lines carrying the rays have at most one intersection C The base must be horizontal D The rays can be stretched until they agree
8

For triangles $HJK$ and $RST$ , you know
$\begin{aligned} \angle H&\cong\angle R \\ HJ&=RS \end{aligned}$
Which additional pair directly supplies the other endpoint-angle pair for ASA using these sides, without calculating another angle?

Answer choices for question 8 A $\angle K\cong\angle T$ B $\angle H\cong\angle S$ C $\angle J\cong\angle T$ D $\angle J\cong\angle S$
9

Triangles $KLM$ and $PQR$ have these given matching parts:
$\begin{aligned} KL&=11 \\ QP&=11 \\ LM&=14 \\ PR&=14 \\ \angle KLM&\cong\angle QPR \end{aligned}$
Which correspondence is established by SAS?

Answer choices for question 9 A
$K\leftrightarrow P$

$L\leftrightarrow Q$

$M\leftrightarrow R$
B
$K\leftrightarrow R$

$L\leftrightarrow Q$

$M\leftrightarrow P$
C
$K\leftrightarrow Q$

$L\leftrightarrow P$

$M\leftrightarrow R$
D
$K\leftrightarrow Q$

$L\leftrightarrow R$

$M\leftrightarrow P$
10

Triangles $ABC$ and $DEF$ have these given matching parts:
$\begin{aligned} \angle A&=35^\circ \\ \angle D&=35^\circ \\ \angle B&=82^\circ \\ \angle E&=82^\circ \\ AB&=15\text{ cm} \\ DE&=15\text{ cm} \end{aligned}$
Which fact explains why ASA applies?

Answer choices for question 10 A The equal 15 cm sides join the two known angle vertices B The third angles must be right angles C The 15 cm sides must be the longest sides D The third side lengths have already been given
11

A base of positive length has intended endpoint angles $68^\circ$ and $112^\circ$ , both drawn into the same half-plane. Why does this not construct a triangle?

Answer choices for question 11 A The base has to be longer than 180 cm B The third angle is also 180 degrees C Every positive base gives a triangle with these angles D The new rays are parallel and never form a third vertex
12

Two triangles have corresponding side lengths $9$ cm and $13$ cm and corresponding included angles $104^\circ$ . One drawing is rotated and the other is reflected. What follows?

Answer choices for question 12 A They cannot be congruent because the angle is obtuse B They are congruent by SAS C Their orientation must be identical before using SAS D Their third sides must be measured before any conclusion

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