Congruence and Similarity

Math ⇒ Geometry

Congruence and Similarity starts at 7 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Congruence and Similarity. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 8

Explain the meaning of 'corresponding parts of congruent triangles are equal' (CPCTC).

Explain the SSS similarity criterion for triangles.

Explain why all circles are similar to each other.

Explain why the SSA condition does not guarantee triangle congruence.

Explain why two squares of different sizes are similar but not congruent.

Given two triangles, △PQR and △XYZ, with PQ = XY, QR = YZ, and ∠Q = ∠Y, are the triangles congruent?

If △ABC ~ △DEF and AB = 4 cm, DE = 8 cm, and the area of △ABC is 10 cm², what is the area of △DEF?

If △ABC ~ △DEF and AB = 6 cm, DE = 9 cm, and BC = 8 cm, what is the length of EF?

If △ABC ≅ △DEF and ∠A = 50°, ∠B = 60°, what is the measure of ∠D?

If two similar triangles have a side ratio of 2:3, what is the ratio of their areas?

If two similar triangles have areas 16 cm² and 64 cm², what is the ratio of their corresponding sides?

If two similar triangles have perimeters 12 cm and 18 cm, what is the ratio of their corresponding sides?

If two triangles have corresponding sides in the ratio 5:7, what is the ratio of their perimeters?

If two triangles have sides in the ratio 3:4:5 and 6:8:10, are they similar?

State the difference between congruent and similar figures.

A rectangle has sides 4 cm and 6 cm. Another rectangle has sides 8 cm and 12 cm. Are these rectangles similar, congruent, or neither?

A triangle has sides of lengths 8 cm, 15 cm, and 17 cm. Another triangle has sides of lengths 16 cm, 30 cm, and 34 cm. Are these triangles congruent, similar, or neither?

Explain why the AAA criterion is not sufficient to prove congruence of triangles.

If two triangles are similar and the ratio of their corresponding medians is 3:5, what is the ratio of their areas?

Two triangles, △ABC and △DEF, have AB = 5 cm, AC = 7 cm, ∠A = 60°, DE = 10 cm, DF = 14 cm, and ∠D = 60°. Are the two triangles similar? Justify your answer.