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 10
A triangle has sides 8 cm, 15 cm, and 17 cm. Another triangle has sides 16 cm, 30 cm, and 34 cm. Are these triangles congruent or similar?
Describe the difference between congruence and similarity in geometric figures.
Explain why all equilateral triangles are similar to each other.
Explain why the AAA criterion is not sufficient for triangle congruence.
A triangle has sides 8 cm, 15 cm, and 17 cm. Another triangle has sides 16 cm, 30 cm, and 34 cm. Are these triangles congruent or similar?
Given two similar triangles, △PQR and △XYZ, with PQ = 6 cm, QR = 8 cm, and XY = 9 cm. What is 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 corresponding sides is 2:3. What is the ratio of their areas?
If △ABC ≅ △DEF, which of the following statements is true?
(1) AB = DE
(2) ∠A = ∠F
(3) BC = EF
(4) AC = DF
Which of the following is a correct similarity criterion for triangles?
(1) SSS
(2) SAS
(3) AA
(4) SSA
Which of the following is a correct statement about congruent triangles?
(1) They have equal corresponding sides and angles
(2) They have equal areas only
(3) They have equal perimeters only
(4) They have equal corresponding angles only
Which of the following is NOT a criterion for triangle congruence?
(1) SSS
(2) SAS
(3) AAA
(4) ASA
Fill in the blank: If two triangles are congruent, the measure of their corresponding angles is ________.
Fill in the blank: If two triangles are congruent, their corresponding ________ are equal.
Fill in the blank: The ________ criterion for triangle congruence requires two angles and the included side to be equal.
Fill in the blank: The ________ criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
If two rectangles have the same area, are they necessarily congruent?
If two triangles have sides in the ratio 3:4:5 and 6:8:10, are they similar?
If two triangles have two pairs of corresponding sides in the same ratio and the included angles are equal, are the triangles similar?
True or False: All congruent figures are also similar.
