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 12

Describe a real-world application where triangle similarity is used.

Describe the SSS (Side-Side-Side) similarity criterion for triangles.

Explain the difference between congruence and similarity in geometric figures.

Explain why the SSA condition does not guarantee triangle congruence.

Given △PQR ~ △XYZ, if PQ = 6 cm, QR = 8 cm, PR = 10 cm, and XY = 9 cm, find the length of YZ.

Given two similar triangles, if the length of a side in the first triangle is 5 cm and the corresponding side in the second triangle is 15 cm, what is the scale factor from the first to the second triangle?

Given two similar triangles, the ratio of their areas is 9:16. What is the ratio of their corresponding sides?

Given two similar triangles, the ratio of their corresponding sides is 2:5. What is the ratio of their areas?

If △ABC ~ △DEF and AB/DE = 3/4, what is the ratio of the area of △ABC to the area of △DEF?

If two polygons are similar, what can be said about the ratio of their perimeters?

If two triangles are similar and the ratio of their perimeters is 5:7, what is the ratio of their corresponding sides?

Prove that if two triangles have their corresponding sides in the same ratio, then their corresponding angles are equal.

State the Side-Angle-Side (SAS) similarity criterion for triangles.