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Converse of BPT - Free MCQ Practice Test with solutions, Class 10


MCQ Practice Test & Solutions: Test: Converse of BPT (10 Questions)

You can prepare effectively for Class 10 Online MCQ Tests for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Converse of BPT". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Test: Converse of BPT - Question 1

In triangle ABC ,DE || BC AD=3 cm, DB = 8 cm AC = 22 cm. At what distance from A does the line DE cut AC?

Detailed Solution: Question 1

In triangle ABC and ADE, Angle A is common and since DE || BC, Angle D= Angle B. So by  AA criterion, ΔABC - ΔADE
So, 

EC=16
AE=AC-EC=6cm

Test: Converse of BPT - Question 2

In a triangle ABC, BC || DE If AD = 1.5, DB = 4.5, AE = 1.3, EC = ?​

Test: Converse of BPT - Question 3

In triangle DEF,GH is a line parallel to EF cutting DE in G and and DF in H. If DE = 16.5, DH = 5, HF = 6 GE = ?

Test: Converse of BPT - Question 4

In triangle ABC, DE || BC, AD = 1.2 cm DB = 3.6 cm, AE = 1.6 cm.What must be the value of EC?​

Test: Converse of BPT - Question 5

In trapezium ABCD a line EF cuts the diagonal AC in O such that AO/OC = 2/3 and EF is parallel to BC.In what ratio does EF cut AB and CD?​

Test: Converse of BPT - Question 6

In the given figure S and T are respectively points on the side PQ and PR of a ΔPQR. If PS = 2.5 cm, PQ = 7.5 cm, PT = 1.7 cm and PR = 5.1 cm then find that which of the following relations definitely holds true

Test: Converse of BPT - Question 7

In triangle MNS, A and B are points on the sides MN, NS respectively.  Then AB is …………………. to NS :​

Detailed Solution: Question 7

In ∆MNS we have,

→ AN = 1/2(MN)
→ AN = (1/2)(MA + AN)
→ AN = (1/2)MA + (1/2)AN
→ AN - (1/2)AN = (1/2)MA
→ AN[1 - (1/2)] = (1/2)MA
→ (1/2)AN = (1/2)MA
→ AN = MA
so, A is mid point of MN .

similarly,
→ BS = (1/2)(MS)

so, B is mid point of MS .

since AB is a line segment joining the mid points of two sides of ∆MNS .

therefore, → AB || NS { According to Mid point theorem the line segment joining the mid points of two sides of a triangle is parallel to the third side . }

Test: Converse of BPT - Question 8

Triangle ABC is an isosceles right triangle right angled at B.DE is a line parallel to BC which intersects AB in D and AC in E.What ratio are the sides of triangle ADE in?

Detailed Solution: Question 8

Since AB =BC and the triangles are similar, AB/AD=BC/DE
Gives AD=DE
So by Pythagoras theorem, 
H2 = P2 + B2
H= 2x2
H = √2x
So the sides are in the ratio x:x: √2x which is 1:1: √2

Test: Converse of BPT - Question 9

Two poles stand on the ground at a distance of 20m and 50 m respectively from a point A on the ground, the taller pole at 30 m from smaller pole. A cable originates from the top pf the taller pole, passing on the other pole ends on a hook at point A. If the length of the cable is 100 m , how much of it lies between the the two poles?

Test: Converse of BPT - Question 10

In triangle MNP a line QR intersects MN and MP in Q and R respectivelysuch that MQ/QN = MR/RP. If ∠MNP = 60°, ∠MPN = 50° What are the values of the angles of the triangle MQR?​

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