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

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.
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
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.


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.

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.


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.


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

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