In the adjoining figure , ∠ 1 = ∠ 2 and ∠ 3 = ∠ 4 . Show that P T × Q R = P R × S T .

From the question it is given that, ∠ 1 = ∠ 2 and ∠ 3 = ∠ 4 Adding ∠ 6 to both LHS and RHS we get ∠ 1 + ∠ 6 = ∠ 2 + ∠ 6 ∠ S P T = ∠ Q P R Consider the △ P Q R and △ P S T , ∠ S P T = ∠ Q P R ∠ 3 = ∠ 4 Therefore, △ P Q R ~ △ P S T We know that two triangles are similar if their corresponding sides are proportional. So, P T P R = S T Q R ⇒ P T × Q R = S T × P R Hence, proved

In the adjoining figure , A B = A C . If P M ⊥ A P , show that P M × P C = P N × P B .

From the given figure, A B = A C If P M ⊥ A B and P N ⊥ A C We have to show that, P M × P C = P N × P B Consider the ∆ A B C , A B = A C ∠ B = ∠ C Then, consider Δ C P N and Δ B P M ∠ N = ∠ M [both angles are equal to 90 ° ] ∠ C = ∠ B [from above] Therefore, Δ C P N ~ Δ B P M [from axiom] So, P C P B = P N P M By cross multiplication we get, P C × P M = P N × P B Therefore, it is proved that,

E M B I B E

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test

Chapter Test

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - Chapter Test

Simple step-by-step solutions to Chapter Test questions of Triangles from CBSE Syllabus Standard Mathematics for Class X. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from Chapter Test with Hints & Solutions

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 5

In the adjoining figure , $∠ 1 = ∠ 2$ and $∠ 3 = ∠ 4$ . Show that $P T \times Q R = P R \times S T .$

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MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 6

In the adjoining figure , $A B = A C .$ If $P M ⊥ A P,$ show that $P M \times P C = P N \times P B .$

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HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 7

In the adjoining trapezium. $A B C D, A B ∥ D C$ . If $A B = 6 c m, D C = 12 c m, C F = 9 c m, A O = 4 c m$ and $B C = 10 c m$ , find $E C, A F$ and $O E$

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HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 8

In the adjoining figure $A D = 4 c m, B D = 11 c m, A E = 6$ and $E C = 4 c m$ . Prove that $△ A D E ~ △ A C B$ . If $∠ A B C = 40 °$ , find $∠ A E D$ . If $D E = 7 c m,$ find $B C .$

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HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 9

In the adjoining quadrilateral $A B C D$ , $A B = A D .$ The bisectors of $∠ B A C$ and $∠ C A D$ meet the sides $B C$ and $D C$ at the points $E$ and $F$ respectively. Prove that $E F$ is parallel to $B D .$

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HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 10

In the adjoining figure , medians $A D$ and $B E$ of $△ A B C$ meet at the point $G,$ and $D F$ is drawn parallel to $B E,$ Prove that $E F = F C$ and $A G : G D = 2 : 1$

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HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 11

Prove that the line segments joining the mid-points of the sides of a triangle form four triangles, each of which is similar to the original triangle.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 7 - Triangles>Chapter Test>Q 18

In the adjoining figure , find the length of $A D$ in terms of $b$ and $c .$

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