RHS Criteria for Congruency

Q.

In the figure, $X$ is a point in the interior of square $ABCD.AXYZ$ is also a square. If $DY=3cm$ and $AZ=2cm,$ then $BY=$

1. $5cm$

2. $6cm$

3. $7cm$

4. $8cm$

Q.

In the figure, $AB\perp BE$ and $FE\perp BE$. If $BC=DE$ and $AB=EF$, then $\Delta ABD$ is congruent to

1. $\Delta ECF$

2. $\Delta CEF$

3. $\Delta FEC$

4. $\Delta EFC$

Q.

Can a triangle have two obtuse angle?give reason for your answer

Q. In a right angled triangle, two sides are 9 cm and 12 cm. Then, the hypotenuse will be:

1. 10 cm
2. 15 cm
3. 13 cm
4. 14 cm

Q.

In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

Q.

It is given that triangle ABC is congruent with triangle FDE and AB is equal to 5 angle, B is equal to 40 degree and Angle A is equal to 80° then which of the following is true

(1) DF=5 , angle F=60

(2) DF=5 , angle E= 60

(3)DF=5 , angle E= 120

(4)DF=5 , angle D= 40

Q. Question 5
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that $\angle ABD=\angle ACD.$

Q.

In the figure, triangle ABC is an isosceles triangle with AB = AC and measure of angle ABC = 50^o. Then the measure of angle BDC and angle BEC will be

1. 40^o, 120^o

2. 60^o, 100^o

3. 50^o, 100^o

4. 80^o, 100^o

Q. In a triangle ABC, D is the midpoint of BC and E is the midpoint of AD. If BE is produced meets AC in F. Then prove that AF is equal to one third of AC.

Q.

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency:

(a) In $\Delta ABC$ and $\Delta DEF$, $AB=DE,BC=EF$ and $\angle B=$$\angle E$ .

(b) In $\Delta ABC$ and $\Delta DEF$, $\angle B=$$\angle E=$ ${90}^0$, $AC=DF$ and $BC=EF$.

(c) In $\Delta ABC$ and $\Delta QRP$ , $AB=QR$, $\angle B=$$\angle R$ and $\angle C=$$\angle P$ .

(d) In $\Delta ABC$ and $\Delta PQR$ , $AB=PQ,AC=PR$ and $BC=QR$.

(e) In $\Delta ABC$ and $\Delta PQR$ , $BC=QR$, $\angle A=$ ${90}^{\circ }$, $\angle C=$ $\angle R=$ ${40}^{\circ }$ and $\angle Q=$${50}^{\circ }$.

Q.

In an isosceles right angled triangle, the measures of the acute angles are

1. 40^o, 50^o

2. 35^o, 55^o

3. 60^o, 30^o

4. 45^o, 45^o

Q.

ABCD is a square, X and Y are points on sides AD and BC respectively such tht AY = BX, Prove that BY = AX and $\angle BAY=\angle ABX.$

Q.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Q.

In Fig. BD and CE are two altitudes of a $\Delta$ ABC such that BD = CE.

Prove that the ABC is an isoceles triangle. [2 MARKS]

Q.

Using the information given in the figure, find the values of x and y.

1. x = 15, y = 9

2. x = 9, y = 15

3. x = 14, y = 9

4. x = 15, y = 10

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:

(i) $\Delta AMC\cong \Delta BMD$

(ii) $\angle DBC$ is a right angle.

(iii) $\Delta DBC\cong \Delta ACB$

(iv) $CM=\frac{1}{2}AB$

Q. Explain RHScongruence rule of triangle.

Q.

In 🔺 PQR, if angle P - angle Q = 42° and angle Q - angle R =21°.Find angle P, angle Q and angle R

Q.

In the given figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).

Q.

In triangle ABC, side AB is produced to D so that BD = BC. If angle B = 60^o and angle A = 70^o, then

1. AD < CD

2. AD ≠ CD

3. AD = CD

4. AD > CD

Q. In Triangle ABC AD is the median. Prove that AB +AC > 2AD.

Q.

ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.

Q.

In the figure, $AD\perp CDandCB\perp CD.IfAQ=BPandDP=CQ,\text{prove that}\angle DAQ=\angle CBP.$

Q.

If perpendiculars from any point within an angle on its arms are congruent, prove tht it lies on the bisector of that angle.

Q.

ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that $\Delta ABC$ is isosceles.

Q. 39.If in Δ ABC , D is the midpoint of sideBC , angle ADB=45^° and angle ACD=30^° , then angle BAD and angle ABC are respectively equal to

Q.

In the given figure, which congruence rule can be used to prove that $△$ABC $\cong$ $△$CDA?

1. ASA congruence rule
2. SAS congruence rule
3. RHS congruence rule
4. SSS congruence rule

Q.

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

1. 1

2. 0.5

3. 1.5

4. 2

Q.

In the given figure, $BA\perp AC,DE\perp DF,$ such that, $BA=DE,BF=EC.$ Then, $△ABC\cong △DEF$ by which congruence rule?

1. SAS

2. SSS
3. RHS

4. ASA

Q.

The hypotenuse of a right angled triangle is 25 cm. The other two sides are such that one is 5 cm longer than the other. Their lengths (in cm) are

1. 10, 15

2. 20, 25

3. 15, 20

4. 25, 30