Similar Triangles — Practice Quiz
Telangana Board · Class 10 · Mathematics
4 MCQs on Similar Triangles for Telangana Board Class 10 Mathematics: tap an answer to check it and see why. The full chapter test has 44 questions.
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Quick Quiz: Similar Triangles
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If triangle ABC is similar to triangle DEF with a scale factor of 2:3, and AB = 6 cm, what is the length of DE?
In triangle PQR, if PQ = 8 cm, QR = 6 cm, and a line segment ST parallel to QR divides the triangle such that PS = 4 cm, what is the length of ST?
If the ratio of areas of two similar triangles is 16:25, what is the ratio of their corresponding sides?
In a right triangle with sides 3 cm, 4 cm, and 5 cm, what is the length of the hypotenuse?
Sample Questions
Which of the following are sufficient conditions to prove two triangles are similar? (Select all correct answers)
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Two angles are equal (AA similarity), All three sides are proportional (SSS similarity), Two sides are proportional and included angle is equal (SAS similarity), All three angles are equal (AAA similarity)
The similarity criteria are: AA (two angles equal), SSS (all sides proportional), SAS (two sides proportional with included angle equal), and AAA (all angles equal, which is equivalent to AA). Having just one side and one angle equal is insufficient for similarity.
If triangle ABC ~ triangle PQR and AB = 6 cm, BC = 8 cm, PQ = 9 cm, then what is QR?
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12 cm
Since triangles are similar, corresponding sides are proportional. AB/PQ = BC/QR, so 6/9 = 8/QR. Cross multiplying: 6 × QR = 8 × 9, so 6 × QR = 72, therefore QR = 12 cm.
The statement 'All congruent triangles are similar' is:
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True
All congruent triangles are similar because they have the same shape and size. If triangles are congruent, their corresponding angles are equal and corresponding sides are in the ratio 1:1, which satisfies the conditions for similarity.
In triangle ABC, DE is parallel to BC. If AD = 3 cm, DB = 6 cm, and AE = 4 cm, what is EC?
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8 cm
By the Basic Proportionality Theorem, AD/DB = AE/EC. Substituting: 3/6 = 4/EC. Cross multiplying: 3 × EC = 6 × 4, so 3 × EC = 24, therefore EC = 8 cm.
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