In the given figure, UB ∥ AT and CU ≡ CB . Prove that △ CUB ~ △ CAT and hence △ CAT is isosceles.

By the given condition, ∠ CUB = ∠ CBU (Since, △ CUB , CU = CB ) In ∆ UCB and ∆ ACT ∠ CUB = ∠ CAB (Since UB ∥ AT , corresponding angles) ∠ CBU = ∠ CTA (Since, UB ∥ AT , corresponding angles) ∠ UCB = ∠ ACT (common angle) So, △ CUB ~ △ CAT (By A A A criteria) Since ∠ CUB = ∠ CBU , ∠ CAT = ∠ CTA . So, CA = CT If sides of the triangle are equal then their opposite angles are also equal and that triangle is isosceles triangle. So, ∆ CAT is an isosceles triangle.

E M B I B E

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 8

HARD

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IMPORTANT

Earn 100

In the given figure $YH ∥ TE$ . Prove that $△ WHY ~ △ WET$ and also find $HE$ and $TE$ .

Important Questions on Geometry

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 9

In the given figure, if $△ EAT ~ △ BUN$ find the measure of all angles.

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 10

In the given figure, $UB ∥ AT$ and $CU \equiv CB$ . Prove that $△ CUB ~ △ CAT$ and hence $△ CAT$ is isosceles.

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EASY

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 11

Two similar triangles will always have _____ angles.

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 12

If in triangles

PQR

and

XYZ, \frac{PQ}{XY} = \frac{QR}{ZX}

then they will be similar if

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 13

A flag pole

15 m

high casts a shadow of

3 m

at

10 a . m

. The shadow cast by a building at the same time is

18.6 m

. The height of the building is

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 14

If

△ ABC ~ △ PQR

in which

∠ A = 53 °

and

∠ Q = 77 °

, then

∠ R

is.

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Exercise 5.1>Q 15

In the given figure, which of the following statements is true?

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IMPORTANT

Standard Eight Mathematics>Chapter 5 - Geometry>Think>Q 1

In any acute angled triangle, all three altitudes are inside the triangle. Where will be the orthocentre? In the interior of the triangle or in its exterior?