Maths-

General

Easy

Question

# Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:

(i) AOD ⩭ BOC

(ii) AD || BC

Hint:

### Find the congruence rule used and then find the parallel sides.

## The correct answer is: AD || BC.

### (i) In ΔAOD and ΔBOC, we have

AO = OB (given)

OD = OC (given)

Since CD and AB intersects, we have

(vertically opposite angles)

So by SAS congruence rule, we have

ΔAOD ⩭ ΔBOC

(ii) SinceΔAOD ⩭ ΔBOC, we have

( Corresponding part of congruent triangles)

But they form alternate interior angles and since they are equal, AD || BC.

### Related Questions to study

Maths-

### Kumar wants to spread a carpet on the floor of his classroom. The floor is a square

with an area of 4160.25 square feet. What is the length of carpet on each side?

### Kumar wants to spread a carpet on the floor of his classroom. The floor is a square

with an area of 4160.25 square feet. What is the length of carpet on each side?

Maths-General

Maths-

### The volume of a cubical box is 12167 cm^{3}. Find the side of the box and its 6 sides area?

### The volume of a cubical box is 12167 cm^{3}. Find the side of the box and its 6 sides area?

Maths-General

Maths-

### The area of a square is 289 m^{2}, find its perimeter?

### The area of a square is 289 m^{2}, find its perimeter?

Maths-General

Maths-

### What is the least seven digits which is a perfect square. Also find the square root of the number so obtained

### What is the least seven digits which is a perfect square. Also find the square root of the number so obtained

Maths-General

Maths-

### Find the least number which must be subtracted from 23416 to make it a perfect square.

### Find the least number which must be subtracted from 23416 to make it a perfect square.

Maths-General

Maths-

### Find the least number which must be added to 732733 to obtain a perfect square.

### Find the least number which must be added to 732733 to obtain a perfect square.

Maths-General

Maths-

### In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:

### In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:

Maths-General

Maths-

### Show that 64 is square as well as cube number

### Show that 64 is square as well as cube number

Maths-General

Maths-

### From the given figures, find by which criteria the two triangles ABC and PQR are congruent.

In the figure XY = PZ. Prove that XZ = PY.

In the figure XY = PZ. Prove that XZ = PY.

### From the given figures, find by which criteria the two triangles ABC and PQR are congruent.

In the figure XY = PZ. Prove that XZ = PY.

In the figure XY = PZ. Prove that XZ = PY.

Maths-General

Maths-

### Evaluate:

### Evaluate:

Maths-General

Maths-

### Evaluate:

### Evaluate:

Maths-General

Maths-

### In the figure above, and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?

### In the figure above, and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?

Maths-General

Maths-

### Find the square-root of the following numbers.

b) 25921

### Find the square-root of the following numbers.

b) 25921

Maths-General

Maths-

### In the figure, AF is perpendicular to BC and AF is the angle bisector of , then state the rule used for the congruence of Δ DAF an ΔEAF.

### In the figure, AF is perpendicular to BC and AF is the angle bisector of , then state the rule used for the congruence of Δ DAF an ΔEAF.

Maths-General

Maths-

### Find the least number by which 85750 must be divided so that the quotient is a perfect cube?

### Find the least number by which 85750 must be divided so that the quotient is a perfect cube?

Maths-General