Congruent Figures Practice
Here are some practice problems on congruent figures:
1. Determine if the following pairs of figures are congruent:
a) Triangle ABC with sides measuring 3 cm, 4 cm, and 5 cm, and Triangle DEF with sides measuring 4 cm, 3 cm, and 5 cm.
b) Rectangle PQRS with length 6 cm and width 4 cm, and Rectangle UVWX with length 4 cm and width 6 cm.
2. Find the missing side lengths in the following congruent triangles:
a) Triangle ABC with side lengths AB = 5 cm, BC = 8 cm, and AC = 7 cm, is congruent to Triangle DEF. Find the length of side DE.
b) Triangle PQR with side lengths PQ = 3 in, QR = 4 in, and PR = 5 in, is congruent to Triangle XYZ. Find the length of side YZ.
3. Based on the given information, determine if the following pairs of figures are congruent:
a) Triangle ABC with sides AB = 3 cm, BC = 4 cm, and AC = 5 cm, and Triangle DEF with sides DE = 3 cm, EF = 4 cm, and FD = 5 cm.
b) Rectangle PQRS with length 6 cm and width 4 cm, and Rectangle UVWX with length 6 cm and width 5 cm.
4. Determine if the following pairs of figures are congruent or similar:
a) Triangle ABC with sides measuring 5 cm, 12 cm, and 13 cm, and Triangle DEF with sides measuring 10 cm, 24 cm, and 26 cm.
b) Rectangle PQRS with length 7 cm and width 9 cm, and Rectangle UVWX with length 14 cm and width 18 cm.
Answers:
1. a) Yes, the triangles are congruent by side-side-side (SSS) congruence.
b) No, the rectangles are not congruent because their lengths and widths are not equal.
2. a) The length of side DE is also 5 cm, based on the congruence of triangles.
b) The length of side YZ is also 3 in, based on the congruence of triangles.
3. a) Yes, the triangles are congruent by side-side-side (SSS) congruence.
b) No, the rectangles are not congruent because their widths are not equal.
4. a) The triangles are similar because their corresponding side lengths are proportional.
b) The rectangles are not congruent or similar because their lengths and widths are not proportional.