Q1
Which similarity criterion states that if two angles of one triangle are equal to two angles of another, the triangles are similar?
📝 SolutionThe AA (Angle-Angle) criterion: if two pairs of corresponding angles are equal, the third pair is automatically equal too, making the triangles similar.
Q2
In $\triangle ABC$, if $D$ and $E$ are midpoints of $AB$ and $AC$ respectively, then $DE$ is:
📝 SolutionThis is the Midpoint Theorem, a special case of the Basic Proportionality Theorem: the line joining midpoints of two sides is parallel to the third side and equal to half of it.
Q3
If $\triangle ABC \sim \triangle DEF$ and the perimeter of $\triangle ABC$ is 30 cm while $\triangle DEF$ is 60 cm, the ratio of corresponding sides is:
📝 SolutionFor similar triangles, the ratio of perimeters equals the ratio of corresponding sides: $\frac{30}{60} = \frac{1}{2}$, i.e. $1:2$.
Q4
Assertion (A): If two triangles are similar, they are also congruent.
Reason (R): Congruent triangles have equal corresponding sides, while similar triangles only need equal corresponding angles and proportional sides.
Choose the correct option:
Reason (R): Congruent triangles have equal corresponding sides, while similar triangles only need equal corresponding angles and proportional sides.
Choose the correct option:
📝 SolutionSimilar triangles need not be congruent — they can differ in size while having the same shape. So A is false. R correctly explains why similarity does not imply congruence, so R is true.
Q5
If in $\triangle ABC$ and $\triangle DEF$, $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$, the similarity criterion used is:
📝 SolutionWhen all three pairs of corresponding sides are in the same ratio, the triangles are similar by the SSS similarity criterion.
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Class 10 · Maths
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