In the given figure, if AD DB = AE EC , prove that AD AB = AP AQ .

Given, AD DB = AE EC To prove: AD AB = AP AQ Proof: We have, AD DB = AE EC ∴ By the converse of Thales theorem DE ∥ BC ⇒ DP is also parallel to BQ In ∆ ABQ , ∵ D P ∥ BQ ⇒ AD AB = AP AQ [By Thales theorem] Hence, proved.

ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ = 1 4 AC . If PQ produced meets BC at R , prove that R is the midpoint of BC .

Given, ABCD is a parallelogram. P is the midpoint of CD . Q is a point on AC such that CQ = 1 4 AC . PQ produced meet BC in R . To prove: R is the midpoint of BC . Construction: Join BD in O . Let BD intersect AC in O . Proof: O is the midpoint of AC as diagonals of a parallelogram bisect each other. Therefore OC = 1 2 AC ⇒ OQ = OC - CQ = 1 2 AC - 1 4 AC = 1 4 AC ⇒ OQ = CQ Therefore, Q is the midpoint of OC . In ∆ OCD , P is the midpoint of CD and Q is the midpoint of OC , Therefore, PQ ∥ OD (By Midpoint Theorem) ⇒ PR ∥ BD In ∆ BCD , P is the midpoint of CD and PR ∥ BD Therefore, R is the midpoint of BC (By the converse of midpoint theorem).

E M B I B E

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE

EXERCISE

Author:J P Mohindru & Bharat Mohindru

J P Mohindru Mathematics Solutions for EXERCISE

Simple step-by-step solutions to EXERCISE questions of Triangles from Modern's abc+ of Mathematics for Class 10. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from EXERCISE with Hints & Solutions

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 4

In $△ ABC$ , $D$ and $E$ are points on sides $AB$ and $AC$ respectively. Determine whether, $DE | | BC$ or not in the following case:

$AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm$

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 4

In $△ ABC$ , $D$ and $E$ are points on the sides $AB$ and $AC$ respectively. Determine whether, $DE | | BC$ or not in the following case:

$AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm$

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 4

In $△ ABC$ , $D$ and $E$ are points on the sides $AB$ and $AC$ respectively. Determine whether, $DE | | BC$ or not in each of the following case:

$AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm$

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 4

$D$ and $E$ are points on the sides $AB$ and $AC$ respectively of a $∆ ABC$ . Determine whether $DE | | BC$ or not in each of the following cases.

$AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 9

In the given figure, if $\frac{AD}{DB} = \frac{AE}{EC}$ , prove that $\frac{AD}{AB} = \frac{AP}{AQ}$ .

Question Image

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 10

$A B C D$ is a quadrilateral. From any point on $A B$ a line is drawn parallel to $B C$ intersecting $A C$ at $Q$ and the line through $Q$ drawn parallel to $C D$ intersect $A D$ at $R$ . Prove that $P R ∥ B D$ .

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 6 - Triangles>EXERCISE>Q 11

$ABCD$ is a parallelogram in which $P$ is the midpoint of $DC$ and $Q$ is a point on $AC$ such that $CQ = \frac{1}{4} AC$ . If $PQ$ produced meets $BC$ at $R$ , prove that $R$ is the midpoint of $BC$ .