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Test: Mid Point Theorem - Class 9 MCQ


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10 Questions MCQ Test Online MCQ Tests for Class 9 - Test: Mid Point Theorem

Test: Mid Point Theorem for Class 9 2024 is part of Online MCQ Tests for Class 9 preparation. The Test: Mid Point Theorem questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Mid Point Theorem MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Mid Point Theorem below.
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Test: Mid Point Theorem - Question 1

D, E, F are midpoints of sides AB, BC and CA of ΔABC, if ar(ΔABC) = 64 cm2 then, area of ΔBDE is:

Detailed Solution for Test: Mid Point Theorem - Question 1

Bcs (ABC) is a full triangle ABC triangle divide into four equal partsTherefore, 64÷4=16 cm2

Test: Mid Point Theorem - Question 2

In the adjoining figure, ABCD and PQRC are rectangles, where Q is the midpoint of AC. Then DP is equal to

Detailed Solution for Test: Mid Point Theorem - Question 2

Given that PQRS and ABCD are rectangle and Q is the mid pt of AC.

Since PQRS and ABCD are rectangle, every angle would be of 90°.

Consider AD and PQ.

angle ADP = 90°
angle QPC = 90°

Now, angle ADP lies corresponding to angle QPC and are equal.

If corresponding angles are equal, then the lines are parallel


=> AD || PQ

Now consider ∆ADC.

Q is the midpoint of AC (Given)
AD || PQ (shown above)

We know that,
line drawn parallel from the midpoint of a side, to other side, bisects the third side.

Hence, P would be the midpoint of DC

Hence, DP = PC

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Test: Mid Point Theorem - Question 3

In triangle ABC, E and F are the mid points of the sides AC and AB respectively. The altitude AP to BC intersects EF at Q. Then

Test: Mid Point Theorem - Question 4

Figure shows that AD and BF are medians of ABC and BF || DE then CE is equal to

Detailed Solution for Test: Mid Point Theorem - Question 4

A median divides the triangle into 2 equal parts. So AD divides the triangle into the triangle ABD & ACD . Further BF divides the triangle into 2 equal parts .
So AF = 1/2 AC
DE bisects it into 2 parts
So EF = 1/2 EC
EF =FC
AF = EC
SO FC =1/2 * 1/2 AC
= 1/4 AC

Test: Mid Point Theorem - Question 5

In ΔABC, D, E and F are respectively mid points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm respectively, the perimeter of DEF will be

Detailed Solution for Test: Mid Point Theorem - Question 5

Since, D,E,F are the midpoints of BC,CA and AB,Thus

Test: Mid Point Theorem - Question 6

If D, E and F are the mid points of the sides BC, CA and AB of an equilateral triangle ABC, then triangle DEF is

Test: Mid Point Theorem - Question 7

The quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a

Test: Mid Point Theorem - Question 8

ABCD is a parallelogram in which P, Q, R and S are the mid points of sides AB, BC CD and DA respectively. Then,

Test: Mid Point Theorem - Question 9

Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm. 

Test: Mid Point Theorem - Question 10

In the adjoining figure, the side AC of ABC is produced to E such that CE = 1/2 AC. If D is the midpoint of BC and ED produced meets AB at F, and CP, DQ are drawn parallel to BA, then FD is

Detailed Solution for Test: Mid Point Theorem - Question 10

Given,
ABC is a triangle.
D is midpoint of BC and DQ is drawn parallel to BA.
Then, Q is midpoint of AC.
∴ AQ = DC
∴ FA parallel to DQ||PC.
AQC, is a transversal so, AQ = QC and FDP also a transveral on them.
∴ FD = DP .......(1) [ intercept theorem]
EC = 1/2 AC = QC
Now, triangle EQD, here C is midpoint of EQ and CP which is parallel to DQ.
And, P is midpoint of DE.
DP = PE..........(2)
Therefore, From (1) and (2)
FD = DP = PE
∴ FD = 1/3 FE

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