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 9

Describe a real-life situation where similar triangles can be used to find the height of an object.

Explain the difference between congruent and similar figures.

Explain why the AAA criterion is not sufficient for triangle congruence.

Given △ABC and △DEF, if AB = DE, BC = EF, and ∠B = ∠E, are the triangles congruent?

Given two rectangles, one with sides 4 cm and 6 cm, and another with sides 8 cm and 12 cm. Are the rectangles similar?

Given two similar triangles, if the ratio of their corresponding sides is 5:7, what is the ratio of their areas?

Given two triangles, △PQR and △XYZ, with PQ = 6 cm, QR = 8 cm, PR = 10 cm, and XY = 9 cm, YZ = 12 cm, XZ = 15 cm. Are the triangles similar?

If △ABC ~ △DEF and AB = 5 cm, DE = 10 cm, and the area of △ABC is 20 cm², what is the area of △DEF?

If △ABC ≅ △DEF and AB = 8 cm, what is the length of DE?

If two right triangles have one acute angle equal, are they similar?

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

If two triangles are congruent, what can you say about their perimeters?

If two triangles are similar and the length of a side in the first triangle is 7 cm, and the corresponding side in the second triangle is 21 cm, what is the scale factor from the first to the second triangle?

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

State the SAS criterion for triangle congruence.

State the SSS criterion for triangle similarity.

A student claims that two triangles with two pairs of equal corresponding angles and one pair of equal corresponding sides are always congruent. Is this claim correct? Explain your reasoning.

A triangle has angles 40°, 60°, and 80°. Another triangle has angles 40°, 60°, and 80°. If the longest side of the first triangle is 10 cm and the longest side of the second triangle is 15 cm, what is the ratio of their areas?

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? Justify your answer.

Given two triangles △ABC and △DEF, where AB/DE = AC/DF = 2/3 and ∠A = ∠D, prove that the triangles are similar and find the ratio of their areas.