RHS Rule

Q. D is the mid-point of the base BC of triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If DM = DN, then the triangle is

1. an isosceles triangle
2. an equilateral triangle
3. a right-angled triangle
4. a scalene triangle

Q. Question 11 (iii)
In $\Delta ABCand\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that AD || CF and AD = CF.

Q. Question 9
Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP=CQ. Show that AC and PQ bisect each other.

Q. Question 9 (i)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

$\Delta APD\cong \Delta CQB$

Q.

Question 14
P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O is its diagonals AC and BD. Show that PQ is bisected at 0.

Thinking Process

Firstly, prove that $\Delta ODPand\Delta OBQ$ are congruent by ASA rule. Further show the required result by CPCT rule.

Q. In the figure given below, $\angle BCD={60}^{\circ }$. Enter the measure of $\angle BDA$ in degrees?

1. 30

Q. Question 9 (iv)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

AQ = CP

Q. Question 9 (i)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

$\Delta APD\cong \Delta CQB$

Q. Question 9 (iii)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

$\Delta AQB\cong \Delta CPD$

Q. Find the length of OC, if CD = 8cm and AD and BC are equal perpendiculars to line segment AB as shown below.

1. 4

Q.

In the following diagram, if AC = AB, then $\frac{CF}{BE}$ is equal to _______.

1. 1

2. 2

3. 0.5

4. 1.5

Q.

O is equidistant from the sides AC and AB. Find the value of x - 3.

1. 3

2. 0

3. 1

4. 2

Q. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
$\Delta AMC\cong \Delta BMD$

Q. $\text{In parallelogram}ABCD,AP\text{and}CQ\text{are perpendicular to diagonal}BD.\text{Statement 1:}\Delta APB\cong \Delta CQD,\text{Statement 2: RHS congruence is applied}$

Pick the correct option.

1. Both statements are correct
2. Both statements are false
3. Statement 1 is correct but 2 is false
4. Statement 1 is false but 2 is correct

Q. The value of $2x$ in the given figure is ________.

1. 3
2. 6
3. 9
4. 0

Q. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
$\Delta AMC\cong \Delta BMD$

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
$\Delta APD\cong \Delta CQB$

Q. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
$\Delta AMC\cong \Delta BMD$

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

$\Delta AQB\cong \Delta CPD$

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
AP = CQ

Q. In the given image, the same ||gm has been represented by diff. colors. Which of the triangles are congruent?

1. 
2. 
3. 

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
AP = CQ

Q. In the given parallelogram ABCD, DP = BQ and $\angle ADP=\angle CBQ$. Which triangle is $\Delta ADP$ congruent to?

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:

AQ = CP

Q. $\text{In parallelogram}ABCD,AP\text{and}CQ\text{are perpendicular to diagonal}BD.\text{It can be proved that:}\text{Statement 1:}\Delta APB\cong \Delta CQD,\text{Statement 2: RHS congruence is applied}$

1. Both statements are correct
2. Both statements are false
3. Statement 1 is correct but 2 is false
4. Statement 1 is false but 2 is correct

Q. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
$\Delta APD\cong \Delta CQB$

Q.

In $\Delta ABD$, AB = AD and AC is perpendicular to BD. State the congruence rule by which $\Delta ACB\cong \Delta ACD$.

1. SAS congruence rule

2. SSS congruence rule

3. RHS congruence rule

4. ASA congruence rule

Q.

In the following diagram, if AC = AB, then $\frac{CF}{BE}$ is equal to _______.

1. 1

2. 2

3. 0.5

4. 1.5

Q.

In the given figure, if D and E are the mid points of sides AB and AC, respectively, and DE is produced to F such that E is the mid point of FD, which of the following options is correct?

1. ΔAED ≅ ΔFEC

2. ΔAED ≅ ΔCFE

3. ΔADE ≅ ΔCEF

4. ΔADE ≅ ΔCFE

Q. BE and CF are 2 equal altitudes of $△$ using congruence rule.Then $△ABC$ is

1. Isosceles Triangle
2. Scalane Triangle
3. Equilateral Triangle
4. None of these