CAT Lines, angles & triangles Questions

Lines and triangles connect angle relationships with length and area. Similarity, congruence and right-triangle properties are useful when the diagram contains repeated shapes or parallel lines.

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Key concepts

• Parallel-line angle relationships
• Triangle similarity and congruence
• Pythagoras and triangle area

CAT lines, angles & triangles practice questions

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Common mistakes

• Assuming triangles are similar because they look alike.
• Using side ratios directly as area ratios for similar triangles.

Practical solving approaches

• Mark all given angles and equal lengths on the diagram.
• Prove similarity before using proportional sides, and square the scale factor when comparing areas.

Lines, angles & triangles FAQs

How do areas of similar triangles compare?

Their areas are in the ratio of the squares of corresponding side lengths.

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CAT Lines, angles & triangles Questions

Lines and triangles connect angle relationships with length and area. Similarity, congruence and right-triangle properties are useful when the diagram contains repeated shapes or parallel lines.

9 free practice questions

Key concepts

• Parallel-line angle relationships
• Triangle similarity and congruence
• Pythagoras and triangle area

CAT lines, angles & triangles practice questions

Question 1Multiple choiceHARD

Question 1

Select the correct alternative from the given choices.

Each question is followed by two statements, A and B. Answer each question using the following instructions. Choose [1], if the question can be answered by one of the statements alone but not by the other. Choose [2], if the question can be answered by using either statement alone. Choose [3], if the question can be answered by using both the statements together, but cannot be answered by using either statement alone. Choose [4], if the question cannot be answered even by using both the statements together.

D, E, F are the mid points of the sides AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimeters?

A. AD = 1 cm, DF = 1 cm and perimeter of DEF = 3 cm

B. Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm.

Choose an answer

A.if the question can be answered by one of the statements alone but not by the other.B.if the question can be answered by using either statement alone.C.if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.D.if the question cannot be answered even by using both the statements together.

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Question 2Multiple choiceHARD

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

Choose an answer

A.17.05B.27.85C.22.45D.32.25E.26.25

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Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?

Choose an answer

A.5B.21C.10D.15E.14

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Question 4Multiple choiceMEDIUM

Question 4

The area of the circumcircle of the triangle is:

Refer to the data below and answer the questions that follow.

An isosceles triangle has the greater side equal to 5 cm. The equal angles are half that of the unequal angle.

Choose an answer

A.

B.

C.

D.

E.

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Question 5Multiple choiceMEDIUM

Question 5

Select the correct alternative from the given choices.

In triangle ABC.  angle B = 90 degrees. BD is perpendicular to AC and length of AB = 7 cm,  BC = 24 cm. Calculate the length of BD

Choose an answer

A.8.72 cmB.9.62 cmC.6.72 cmD.7.22 cm

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Question 6Multiple choiceMEDIUM

Question 6

Select the correct alternative from the given choices

Choose an answer

A.6.75 cmB.5.25 cmC.10 cmD.9.67 cm

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Question 7Multiple choiceMEDIUM

Question 7

Select the correct alternative from the given choices

Anil and Vinit are walking towards each other at night. The heights of Anil and Vinit are 1.8 m and 1.5 m respectively. There are
lamp posts behind both of them, the lamp post behind Anil being 6 m high and that behind Vinit being 5 m high. Anil and Vinit and
both the poles lie on a straight line. At a certain moment when they reach 0.9 m apart from each other, they find that the shadows
of their heads fall exactly at each others feet. (i.e., Anil’s head’s shadow falls on Vinit’s feet and Vinit’s head’s shadow falls on Anil’s
feet) How far apart are the two lamp posts?

Choose an answer

A.3.0 mB.1.8 mC.5.1 mD.6.0 m

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Question 8Type in the answerMEDIUM

Question 8

Enter your response (as an integer) using the virtual keyboard in the box provided.

Your answer

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Question 9Multiple choiceMEDIUM

Question 9

Select the correct alternative from the given choices

A piece of paper in the shape of a right-angled triangle having an area of 24 sq cm is cut along a line parallel to the hypotenuse of the
triangle. The length of the hypotenuse of the paper that is left over after cutting is 30% less than the length of the hypotenuse of
the original paper. What is the area (in cm ) of the paper that is left over after cutting?

Choose an answer

A.13.64B.12.64C.11.76D.10.76

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Common mistakes

• Assuming triangles are similar because they look alike.
• Using side ratios directly as area ratios for similar triangles.

Practical solving approaches

• Mark all given angles and equal lengths on the diagram.
• Prove similarity before using proportional sides, and square the scale factor when comparing areas.

Lines, angles & triangles FAQs

How do areas of similar triangles compare?

Their areas are in the ratio of the squares of corresponding side lengths.

More Geometry practice

• Circles →
• Coordinate geometry →
• Mensuration (3D solids) →
• Quadrilaterals & polygons →