Question types

Triangles question types

210 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

210
Questions
6
Question groups
5
Question types
Sample Questions

Triangles questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

$\triangle ABC \sim \triangle DFE . \angle A =40^{\circ}$, then $\angle E +\angle F =$ _______
  • A
    $40^{\circ}$
  • B
    $80^{\circ}$
  • $140^{\circ}$
  • D
    $180^{\circ}$

Answer: C.

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PQ || RS in trapezium PQRS and PR and QS intersect at point O. IF OP=6, OQ = 9 and OR = 8 then OS = ____________ .
  • A
    $\frac{58}{9}$
  • 12
  • C
    $\frac{58}{8}$
  • D
    11

Answer: B.

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In the figure, altitudes $AD$ and $CE$ of $\triangle$ABC intersect each other at the point $P$. Show that: $\vartriangle PDC \sim \vartriangle BEC$
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In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P$. Show that: $\vartriangle AEP \sim \vartriangle ADB$
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In the figure, altitudes AD and CE of $\triangle$ABC intersect each other at the point P. Show that: $\vartriangle ABD \sim \vartriangle CBE$
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In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P$. Show that: $\vartriangle AEP \sim \vartriangle CDP$
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State the pair of triangles in the figure below are similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
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In the figure, $ABC$ and $AMP$ are two right triangles, right angled at $B$ and $M$ respectively. Prove that:
  1. $\triangle ABC \sim \triangle AMP$
  2. $\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}$
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In the figure, $ABC$ and $AMP$ are two right triangles, right angled at $B$ and $M$ respectively. Prove that:
  1. $\triangle ABC \sim \triangle AMP$
  2. $\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}$
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Q 213 Marks Question3 Marks
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio $($or proportion$)$ and hence the two triangles are similar:
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Q 243 Marks Question3 Marks
If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR,$ respectively where $\triangle   ABC \sim \triangle PQR$, Prove that $\frac{{AB}}{{PQ}} = \frac{{AD}}{{PM}}$
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Q 253 Marks Question3 Marks
A vertical pole of length $6\ m$ casts a shadow $4 \ m$ long on the ground and at the same time a tower casts a shadow $28\ m$ long. Find the height of the tower.
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If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
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If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR,$ respectively where $\triangle ABC \sim \triangle PQR,$ Prove that $\frac{{AB}}{{PQ}} = \frac{{AD}}{{PM}}$
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A vertical pole of length $6\ m$ casts a shadow $4\ m$ long on the ground and at the same time a tower casts a shadow $28\ m$ long. Find the height of the tower.
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Sides $AB$ and $AC$ and median $AD$ of a triangle $ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of another triangle $PQR.$ Show that $\Delta A B C \sim \Delta P Q R$.
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$CD$ and $GH$ are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that $D$ and $H$ lie on sides $AB$ and $FE$ of $\triangle ABC$ and $\triangle EFG$ respectively. If $\triangle ABC  \sim \triangle FEG,$ show that:
  1. $\frac{C D}{G H}=\frac{A C}{F G}$
  2. $\triangle DCB \sim\triangle HGE$
  3. $\triangle DCA \sim\triangle HGF$
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