# 9th Class Math Chapter 14 Ratio & Proportions Short Questions Answer

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## 9th Class Math Chapter 14 Ratio & Proportions Short Questions Answer

Define the following: Ratio, Proportion, Congruent Triangles, Similar Triangle

Solution:
Ratio
The ratio of two quantities a and b of same kind is denoted as a:b and is defined as: The ratio a:b = a/b is the Comparison of two like a and b quantities ‘a’ and ‘b’ are called terms of ‘a’ ratio ‘b’. Terms must be expressed in the same units.
Proportion:
The statement of equality of two ratios is called proportion i.e. if a:b = c:d then a, b, c and d are said to be in proportion.
Congruent Triangles:

Two triangles said to be congruent written symbolically as≅, if there exists a correspondence between them such that all the corresponding sides and angles are congruent.
if AB≅ DE A≅ ∠D
BC≅EF and B≅∠E
CA≅FD C≅∠F
Then ∆ABC ≅ ∆DEF
Similar Triangle
If in ∆ABC ↔ ∆DEF
∠A ≅D, ∠B ≅ ∠E, ∠C ≅ ∠F
and AB/DE = BC/EF = CA/FD
Then ∆ABC and ∆DEF are called a similar triangle which is symbolically written as ∆ABC – ∆DEF.

In LMN shown in the figure, MN ‖ PQ.

Solution:

If m LM = 5cm, mLP = 2.5cm, m LQ = 2.3cm, m LN = ?
As PQ ‖ MN
mLP/mLM = mLQ/mLN
2.5/5 = 2.3/mLN
2.5(mLN) = 2.3 x 5 = 11.5
mLN = 11.5/2.5 = 115/25 = 23/5 = 4.6cm
If mLM = 6cm, m LQ = 2.5cm, mQN = 5cm, m LP = ?
As PQ ‖ MN
mLP/mLM = mLQ/mLN
mLP/6 = 2.5/7.2
mLP/6 = 2.5/7.5 x 6 = 25/75 x 6 = 2cm

In the shown figure, let mPA = 8x – 7, m PB = 4x – 3, m AQ = 5x – 3, m BR = 3x – 1. Find the value of x if AB ‖ QR.

Solution:
mPA = 8x – 7, mPB = 4x – 3
mAQ = 5x – 3, m BR = 3x – 1
As AB ‖ QR
mPA/mAQ = mPB/mBR
8x–7/5x–23 = 4x–3/3x–1

(8x–7)(3x–1) = (4x–3)/(5x–3)
24x² – 8x – 21x + 7 = 20x² – 12x – 15x + 9
24x² – 20x² – 29x + 27x + 7 = 9
4x² – 2x + 7 = 9
4x² – 2x – 2 = 0
2x² – x – 1 = 0
2x² – 2x + x – 1 = 0
2x (x – 1) + (x – 1) = 0
(x – 1) (2x + 1) = 0
(x = 1, – ½ )
x = 1 is the required value.

In ∆LMN shown in the figure, LA bisects ∠L. If m LN = 4, m LM = 6, m MN = 8, then find m MA and m AN.

Solution:

mLN = 4, mLM = 6, mMN = 8
LA bisects ∠L
mMA/mNA = mLM/mLN = 6/4
i.e. mMA : mNA = 6:4
but mMN : mMA + mAN = 8
mMA = 6/10 x 8 = 48/10 = 4.8
and mAN = 4/10 x 8 = 32/10 = 3.2

In isosceles ∆PQR shown in the figure, find the value of x and y.

Solution:

PQ ≅ PR
⟹ x = 10cm
PM ? QR Where PQR is an isosceles triangle
∴ mMQ = mMR
⟹ y = 6cm

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