SAS Congruence

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Show your work for each problem.

1.
In $\triangle ABC$ , which angle is included between the sides $AB$ and $BC$ ?
1. a)None of them
2. b) $\angle A$
3. c) $\angle C$
4. d) $\angle B$
2.
Which information proves $\triangle ABC \cong \triangle DEF$ by SAS?
1. a) $AB = DE$ , $BC = EF$ , $CA = FD$
2. b) $AB = DE$ , $\angle B = \angle E$ , $BC = EF$
3. c) $\angle A = \angle D$ , $\angle B = \angle E$ , $AB = DE$
4. d) $AB = DE$ , $BC = EF$ , $\angle A = \angle D$
3.
$\triangle ABC$ and $\triangle DEF$ have $AB = DE = 5$ cm, $\angle B = \angle E = 90°$ and $BC = EF = 12$ cm. In $\triangle ABC$ , $AC = 13$ cm. How long is $DF$ , in cm?
4.
Segments $AE$ and $BD$ cross at $C$ . $\angle ACB = 48°$ . What is $\angle DCE$ , in degrees?
5.
Two triangles have two pairs of equal sides and one pair of equal angles, but the angle is not between the equal sides. What can you conclude?
1. a)Congruent by ASA
2. b)Nothing for sure: this is SSA
3. c)Congruent by SAS
4. d)Congruent by SSS
6.
In $\triangle PQR$ and $\triangle XYZ$ : $PQ = XY$ , $\angle Q = \angle Y$ and $\angle R = \angle Z$ . Which criterion proves $\triangle PQR \cong \triangle XYZ$ ?
1. a)SSS
2. b)ASA
3. c)AAS
4. d)SAS
7.
In $\triangle ABC$ and $\triangle DEF$ : $AB = DE$ , $AC = DF$ and $\angle A = \angle D$ . Which statement is correct?
1. a) $\triangle ABC \cong \triangle DEF$ by SAS
2. b) $\triangle ABC \cong \triangle EDF$ by SAS
3. c) $\triangle ABC \cong \triangle DFE$ by SAS
4. d)Not enough information: this is SSA
8.
In quadrilateral $ABCD$ , $AB = CB$ and $\angle ABD = \angle CBD$ . If $\angle BAD = 95°$ , what is $\angle BCD$ , in degrees?
9.
Segments $AE$ and $BD$ cross at $C$ , the midpoint of both. $AB = 3x + 1$ and $ED = 2x + 6$ (in cm). Find $x$ .
10.
How many different triangles $ABC$ have $\angle A = 30°$ , $AB = 12$ and $BC = 8$ ?
11.
$\triangle ABC$ : $AB = BC = 7$ cm and $\angle B = 40°$ . $\triangle DEF$ : $DE = EF = 7$ cm and $\angle E = 40°$ . Find $\angle D$ .
12.
Segments $AE$ and $BD$ cross at $C$ , with $AC = CE = 6$ cm and $BC = CD = 4$ cm. If $AB = 8$ cm, how long is $DE$ ?
13.
In quadrilateral $ABCD$ : $AB = AD$ , $\angle BAC = \angle DAC = 32°$ and $\angle ABC = 118°$ . Find $\angle BCD$ .
14.
$\triangle ABC$ and $\triangle DEF$ have $AB = DE = 6$ cm, $\angle B = \angle E = 90°$ and $BC = EF = 8$ cm. Find the perimeter of $\triangle DEF$ .
15.
$\triangle PQR$ and $\triangle STU$ have $PQ = ST = 10$ and $\angle Q = \angle T = 55°$ . Also $QR = 2y + 3$ and $TU = 15$ . For which $y$ are the triangles congruent by SAS?
16.
Two different triangles have $\angle A = 30°$ , $AB = 8$ and $BC = 5$ . How much longer is $AC$ in the larger triangle than in the smaller one?
17.
The diagonals $AC$ and $BD$ of quadrilateral $ABCD$ cross at $M$ , the midpoint of both. $AM = 4.5$ cm, $AB = 8$ cm and $BC = 5$ cm. Find the perimeter of $ABCD$ .
18.
Four pairs of triangles are described below. For each pair, decide whether the triangles are guaranteed to be congruent, then count how many pairs are.