SSS Congruence

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Show your work for each problem.

1.
Which information is enough to prove two triangles congruent by SSS?
1. a)Two pairs of equal sides
2. b)Three pairs of equal angles
3. c)Three pairs of equal sides
4. d)Equal perimeters
2.
$\triangle ABC \cong \triangle DEF$ by SSS. $AB = 7$ , $BC = 9$ and $CA = 4$ . How long is $EF$ ?
3.
One triangle has sides 5 cm, 6 cm and 8 cm. Another has sides 6 cm, 8 cm and 5 cm. Are they congruent?
1. a)Only if both are right triangles
2. b)No, the sides are in a different order
3. c)No, an angle is also needed
4. d)Yes, by SSS
4.
Find the length of the side from $A(1, 2)$ to $B(4, 6)$ .
5.
In $\triangle ABC$ : $AB = 6$ , $BC = 10$ , $CA = 8$ . In $\triangle PQR$ : $PQ = 8$ , $QR = 10$ , $RP = 6$ . Check whether the triangles are congruent by SSS.
6.
$\triangle ABC \cong \triangle DEF$ by SSS. $DE = 12$ , $EF = 15$ and $FD = 9$ . What is the perimeter of $\triangle ABC$ ?
7.
In $\triangle KLM$ : $KL = 6$ , $LM = 10$ , $MK = 7$ . In $\triangle STU$ : $ST = 10$ , $TU = 7$ , $US = 6$ . Which congruence statement is correct?
1. a) $\triangle KLM \cong \triangle STU$
2. b) $\triangle KLM \cong \triangle SUT$
3. c) $\triangle KLM \cong \triangle UST$
4. d) $\triangle KLM \cong \triangle TUS$
8.
A side of a triangle goes from $C(-2, 3)$ to $D(4, -5)$ . How long is it?
9.
$\triangle ABC$ has $A(0, 0)$ , $B(3, 0)$ , $C(0, 4)$ . $\triangle DEF$ has $D(5, 1)$ , $E(5, 4)$ , $F(1, 1)$ . Use the distance formula to check SSS.
10.
$\triangle ABC \cong \triangle DEF$ by SSS. $AB = 3x - 4$ , $DE = x + 6$ , $BC = 2y + 1$ and $EF = 15$ . Find $x$ , $AB$ and $y$ .
11.
A square and a rhombus both have four sides of length 4, but they are not congruent. Why does this not contradict SSS?
1. a)Quadrilaterals are not rigid: equal sides do not fix the angles
2. b)Their sides are not really equal
3. c)SSS only works for right triangles
4. d)A rhombus has five sides
12.
In the parallelogram $ABCD$ , $AB = CD = 7$ , $BC = DA = 8$ and the diagonal $AC = 13$ . $\angle ABC = 120°$ . Show that $\triangle ABC \cong \triangle CDA$ and find $\angle CDA$ .
13.
$\triangle ABC \cong \triangle DEF$ by SSS, with $D(1, 2)$ and $E(7, 10)$ . How long is $AB$ ?
14.
$\triangle ABC$ has $A(1, 1)$ , $B(4, 2)$ , $C(2, 5)$ and $\triangle PQR$ has $P(6, -1)$ , $Q(5, -4)$ , $R(2, -2)$ . Compare the squared side lengths to decide whether $\triangle ABC \cong \triangle PQR$ .
15.
Which triangle is congruent to the triangle with vertices $(0, 0)$ , $(4, 0)$ and $(0, 3)$ ?
1. a) $(0, 0)$ , $(5, 0)$ , $(0, 3)$
2. b) $(0, 0)$ , $(6, 0)$ , $(0, 8)$
3. c) $(1, 1)$ , $(5, 1)$ , $(1, 5)$
4. d) $(2, 2)$ , $(2, 6)$ , $(5, 2)$
16.
$\triangle PQR \cong \triangle STU$ by SSS. $PQ = 2x + 3$ , $ST = 4x - 7$ , $QR = x + y$ , $TU = 12$ and $RP = SU = 10$ . Find the perimeter of $\triangle PQR$ .
17.
In the kite $ABCD$ , $AB = AD$ and $CB = CD$ . $\angle BAD = 76°$ and $\angle ABC = 110°$ . Use SSS on $\triangle ABC$ and $\triangle ADC$ to find $\angle BAC$ and $\angle ADC$ .
18.
A square frame with sides of 5 cm has hinges at its corners. It is pushed into a rhombus with an angle of $60°$ . Explain with numbers why SSS cannot work for quadrilaterals and how a brace fixes it.