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Triangles

All 6 textbook questions with direct answer previews. Open any question for simple explanations and exam-ready answers.

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6
Q1

What are similar triangles? How are they different from congruent triangles?

Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional. Congruent triangles have the same shape and the same size.
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Q2

State the Basic Proportionality Theorem.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then it divides those two sides in the same ratio.
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Q3

State the AA similarity criterion for triangles.

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
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Q4

State the SSS and SAS similarity criteria.

SSS: If corresponding sides of two triangles are proportional, the triangles are similar. SAS: If one angle is equal and the including sides are proportional, the triangles are similar.
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Q5

What is the theorem on areas of similar triangles?

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. If △ABC∼△PQR\triangle ABC\sim\triangle PQR, then ar(ABC)ar(PQR)=(ABPQ)2\frac{\text{ar}(ABC)}{\text{ar}(PQR)}=\left(\frac{AB}{PQ}\right)^2.
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Q6

State Pythagoras theorem and its converse.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c2=a2+b2c^2=a^2+b^2. Conversely, if one side square equals the sum of squares of the other two sides, the triangle is right-angled.
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