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Triangle Congruence and SSS: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

For scalene triangles,
$\begin{aligned} AB&=WX \\ AB&=9 \\ BC&=XY \\ BC&=13 \\ AC&=WY \\ AC&=15. \end{aligned}$
Which order records the correspondence supplied by these side pairs?

Answer choices for question 1 A $\triangle BAC\cong\triangle WXY$ B $\triangle BAC\cong\triangle XWY$ C $\triangle BAC\cong\triangle YWX$ D $\triangle BAC\cong\triangle XYW$
2

The given congruence and side lengths are
$\begin{aligned} \triangle KLM&\cong\triangle QPR. \\ KL&=3x+2. \\ QP&=23. \end{aligned}$
What is $x$ ?

Answer choices for question 2 A $\frac{25}{3}$ B $21$ C $\frac{23}{3}$ D $7$
3

Triangles ABC and DEF have
$\begin{aligned} AB&=DE \\ AC&=DF. \end{aligned}$
Which extra equality completes an SSS argument in that order?

Answer choices for question 3 A $BC=EF$ B $BC=DE$ C $AB=EF$ D $m\angle A=m\angle D$
4

Base $AB$ is fixed. Two circles, centered at $A$ and $B$ with fixed positive radii, meet at $C$ above the base line and $C'$ below it. What is the relationship between the triangles $ABC$ and $ABC'$ ?

Answer choices for question 4 A They must have different perimeters B Only the upper one is a triangle C They are reflected, congruent triangles D They have different lengths from each base endpoint
5

Use this ordered congruence and these angle measures:
$\begin{aligned} \triangle JKL&\cong\triangle RST \\ m\angle J&=36^\circ \\ m\angle K&=81^\circ \end{aligned}$
Find $m\angle T$ .

Answer choices for question 5 A $36^\circ$ B $63^\circ$ C $81^\circ$ D $117^\circ$
6

Triangle $ABC$ is congruent to triangle $DEF$ in that order. Which statement is guaranteed even if the second triangle is drawn upside down?

Answer choices for question 6 A $AC=DF$ B $AB=EF$ C $BC=DF$ D $m\angle A=m\angle F$
7

Which pair of actual triangles must be congruent from the side lengths given?

Answer choices for question 7 A Sides 8, 14, 17 cm and sides 8, 14, 16 cm B Sides 8, 14, 17 cm and sides 9, 13, 17 cm C Sides 8, 14, 17 cm and sides 16, 28, 34 cm D Sides 8, 14, 17 cm and sides 17, 8, 14 cm
8

The ordered congruence is
$\begin{aligned} \triangle ABC&\cong\triangle XYZ. \end{aligned}$
The corresponding lengths are
$\begin{aligned} AB&=2t+3. \\ XY&=t+12. \end{aligned}$
What common length do they have?

Answer choices for question 8 A $9$ B $18$ C $21$ D $12$
9

Two four-sided hinged frames have four matching side lengths, but one frame has a corner angle that does not occur anywhere in the other frame. What can be concluded?

Answer choices for question 9 A They are congruent by SSS B They are congruent because four exceeds three C They are not congruent; rigid motions preserve angles D Every four-sided figure with those lengths has the same angles
10

In a construction of $\triangle EFG$ , the base $EF$ is drawn first and $G$ is an intersection of arcs centered at $E$ and $F$ . Which fact justifies $EG$ having the chosen radius?

Answer choices for question 10 A Every point on a circle is that radius from its center B Every arc has the same length as its radius C The straightedge measures the angle at E D The two circles must have equal radii
11

A rigid motion sends $A$ to $D$ , $B$ to $F$ , and $C$ to $E$ . Which statement records this match?

Answer choices for question 11 A $\triangle ABC\cong\triangle DEF$ B $\triangle ABC\cong\triangle DFE$ C $\triangle ACB\cong\triangle DFE$ D $\triangle BAC\cong\triangle DEF$
12

During a three-side construction, the two arcs touch at a point on the base line. What has been constructed?

Answer choices for question 12 A A triangle with a zero-degree corner that still qualifies B Two noncongruent triangles C A triangle needing only a rotation to become noncollinear D A collinear arrangement, not a triangle

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