# Mid Point and Intercept Theorem RS Aggarwal ICSE Class-9th Goyal

**Mid Point and Intercept Theorem** RS Aggarwal ICSE Class-9th Mathematics Solutions Goyal Brothers Prakashan Chapter-9. We provide step by step Solutions of Exercise / lesson-9 **Mid Point and Intercept** Theorem for ICSE Class-9 RS Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe-9 A to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9 Mathematics. it is used in solving geometry problems related to triangles. So let us study the midpoint theorem and equal intercept theorem in detail by solving RS Aggarwal Class-9 ICSE Maths Questions.

**Mid Point and Intercept Theorem** RS Aggarwal ICSE Class-9th Mathematics Solutions Goyal Brothers Prakashan Chapter-9

### Mid Point Theorem

The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

### The converse of Mid Point Theorem

The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.

### Equal Intercept Theorem

The theorem states if a transversal makes **equal intercepts** on three or more parallel lines, then any other line cutting them will also make **equal intercepts**. It means that given any three mutually perpendicular lines, a line passing through them forms intercepts in the corresponding ratio of the distances between the lines.

### Exercise – 9

Question 1

in the given figure D E F are the mid point of side BC CA and AB respectively

(i) if AB= 6.2 find DE

(ii) if DF= 3.8 find AC

(i) if Perimeter of ABC is 21 cm find FE

Answer

Question 2

………LMN is a ……………..find

…………….

………………

Answer

Question 3

………….D E F are ………………….ABCD is a parallelogram

Answer

Question 4

if D E F are ……………. equilateral triangle

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Question 5

………….. ABCD is a quadrilateral ……………PQRS is a rhombus

Answer

Question 6

……………… mid of BC

Answer

Question 7

……. adjoining figure ……………kite prove that

(i) ……………….

(ii) ………………H bisect CB

Answer

Question 8

…… ABCD is ……………….AB at F

Answer

Question 9

……………. AD is median ………………AF= 1/3 of AC

Answer

Question 10

In the adjoining figure .ABC is a right …………….. PA=PB=PC

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Question 11

show ………………….. rhombus

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Question 12

show that ………………….rectangle.

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Question 13

show ……………..square

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Question 14

In the adjoining figure ABCD trapezium …………. MN= 1/2 (AB-CD)

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Question 15

In the adjoining figure …………….. mid of BC

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Question 16

two point …………………. CD = CE

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Question 17

prove that straight line joining the mid points of opposite side of a quadrilateral bisect each other.

Answer

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