# RHS Criteria for Congruency

## Trending Questions

**Q.**

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

5 cm

6 cm

7 cm

8 cm

**Q.**

In the figure, AB⊥ BE and FE⊥ BE. If BC=DE and AB=EF, then Δ ABD is congruent to

ΔECF

ΔCEF

ΔFEC

ΔEFC

**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:

- 10 cm
- 15 cm
- 13 cm
- 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 ∠ ABD=∠ 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

40

^{o}, 120^{o}60

^{o}, 100^{o}50

^{o}, 100^{o}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 ΔABC and ΔDEF, AB=DE, BC=EF and ∠B=∠E .

(b) In ΔABC and ΔDEF, ∠B=∠E= 900, AC=DF and BC=EF.

(c) In ΔABC and ΔQRP , AB=QR, ∠B=∠R and ∠C=∠P .

(d) In ΔABC and ΔPQR , AB=PQ, AC=PR and BC=QR.

(e) In ΔABC and ΔPQR , BC=QR, ∠A= 90∘, ∠C= ∠R= 40∘ and ∠Q=50∘.

**Q.**

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

40

^{o}, 50^{o}35

^{o}, 55^{o}60

^{o}, 30^{o}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 ∠BAY=∠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 Δ 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.

x = 15, y = 9

x = 9, y = 15

x = 14, y = 9

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) ΔAMC≅ΔBMD

(ii) ∠DBC is a right angle.

(iii) ΔDBC≅ΔACB

(iv) CM=12AB

**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

AD < CD

AD ≠ CD

AD = CD

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⊥ CD and CB⊥ CD.If AQ=BP and DP=CQ, prove that ∠DAQ=∠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 ΔABC 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 ≅ △CDA?

- ASA congruence rule
- SAS congruence rule
- RHS congruence rule
- SSS congruence rule

**Q.**

In the following diagram, if AC = AB, then CFBE is equal to _______.

1

0.5

1.5

2

**Q.**

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

SAS

- SSS
- RHS
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

10, 15

20, 25

15, 20

25, 30