In the given figure, if A D D C = B E E C and ∠ C D E = ∠ C E D , then prove that △ C A B is isosceles triangle.

Given: AD DC = BE EC and ∠CDE=∠CED . AD DC = BE EC ∴ By converse of basic proportionality theorem, DE∥AB ⇒∠CDE=∠CAB and ∠CED=∠CBA .......(i) (corresponding angles) Given that, ∠CDE=∠CED ......(ii) From equation (i) and (ii) we can write, ∠CAB=∠CBA . Hence, △CAB is an isosceles triangle. Hence, Proved.

E M B I B E

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 14

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10th ICSE

IMPORTANT

Earn 100

$△ {ABC}_{}$ and $△ AMP$ are two right-angled triangles, right-angled at $B$ and $M$ , respectively. Prove that $CA \times MP = PA \times BC .$

Important Questions on Similarity

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 15

In a

△ ABC, P

and

Q

are points in

AB

and

AC

, respectively and

PQ ∥ BC

. Prove that the median bisects

PQ

.

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IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 16

In the given figure, find the value of $x$ , if $DE ∥ BC$ . Write the answer in centimeter.

Question Image

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 17

In

△ ABC

,

P and Q

are points on

AB

and

AC

such that

PQ ∥ BC

. If

AP = 4 cm, AQ = 3 cm

and

PB = 2 cm

, then find the value of

AC

. Write the answer in centimeters.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 19

In the given figure, if $\frac{A D}{D C} = \frac{B E}{E C}$ and $∠ C D E = ∠ C E D$ , then prove that $△ C A B$ is isosceles triangle.

Question Image

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 1

Suppose

∆ ABC and ∆ DEF

are similar. Area of

∆ ABC is 9 {cm}^{2}

and area of

∆ DEF is 64 {cm}^{2}

. If

DE = 5.1 cm

, then find the value of

AB

.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 2

Suppose

∆ ABC and ∆ DEF

are similar

AB = \frac{1}{3} DE

, then find

ar (∆ ABC) : ar (∆ DEF)

.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 13 - Similarity>Topic Exercise>Q 3

In the given figure, $S and T$ are the points on the sides $PQ and PR$ respectively of $∆ PQR$ , such that $PT = 2 cm, TR = 4 cm and ST ∥ QR$ . Find the ratio of the areas of $∆ PST and ∆ PQR$ .