Test: Converse of BPT - Class 10 MCQ

# Test: Converse of BPT - Class 10 MCQ

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## 10 Questions MCQ Test Online MCQ Tests for Class 10 - Test: Converse of BPT

Test: Converse of BPT for Class 10 2024 is part of Online MCQ Tests for Class 10 preparation. The Test: Converse of BPT questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Converse of BPT MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Converse of BPT below.
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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 for Test: Converse of BPT - 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 = ?​

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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 for Test: Converse of BPT - 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 for Test: Converse of BPT - Question 8

Since AB =BC and the triangles are similar, AB/AD=BC/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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