RHS Criteria for Congruency

Q.

In a right angle triangle the ratio of acute angles is 2 : 1. What are the angles of the triangle.

Q.

Two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle. What is this condition called?

1. SSS congruence condition

2. ASA congruence condition

3. SAS congruence condition

4. RHS congruence condition

Q.

In an isosceles triangle PQR, PQ = PR and angle Q measures 40^o then the measure of angle P is:

1. 140^o

2. 60^o

3. 100^o

4. 80^o

Q. Why are AAA , AAS and SSA not valid as rules of congruency?

Q. if triangle ABE is equal and similar to triangle ACD , show that triangle ADE~ABC

Q.

If two right-angled triangles have their hypotenuses and one side equal,
then the two triangles are congruent by SAS congruence rule.

1. True

2. False

Q. State True or False.
Isosceles triangle has only acute angles.

Q.

Question 158

In the given figure, state the three pairs of equal parts in $\Delta ABC$ and $\Delta EOD$. Is $\Delta ABC\cong \Delta EOD$? Why?

Q. E is a point on side CB produced of an isosceles triangle ABC with AB=AC. if AD perpendicular BC and EF perpendicular AC, prove that triangle ABD~ECF

Q. Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and the leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.The given statement is known as:

1. $SSS$ congruence of two triangles
2. $ASA$ congruence of two triangles
3. $SAS$ congruence of two triangles
4. $RHS$ congruence of two right-angled triangles

Q. Q.What is the meaning of `bisect?

Q. Triangle ABC is right angled at A. If AB = AC, then find the measures of angle B and angle C.

1. angle B = angle C = 90°
2. angle B = angle C = 65°
3. angle B = 35° and angle C = 55°
4. angle B = angle C = 45°

Q.

Two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the corresponding leg of the other triangle. What is this condition called?

1. ASA

2. RHS

3. SAS

4. SSS

Q.

If $BCDE$ is congruent to $OPQR$, then $DE$ is congruent to _____.

1. $\overline{QR}$

2. $\overline{PQ}$

3. $\overline{OR}$

4. $\overline{OP}$

Q.

Question 154 (i)

In the given figure, $QS\perp PR,RT\perp PQ$ and $QS=RT$
Is $\Delta QSR\cong \Delta RTQ$? Give reason.

Q. I is the incentre of triangle ABC.X and Y are the feet of the perpendiculars from A to BI and CI. Prove that XY is parallel to BC.

Q.

In a triangle ABC, right angled at A, AB = AC. Find the value of angle B and angle C.

1. angle B = angle C = 90 degrees

2. angle B = angle C = 65 degrees

3. angle B = 35 degrees and angle C = 55 degrees

4. angle B = angle C = 45 degrees

Q.

In the following figure, if AC = 10 cm and BC = 7 cm then AB is:

1. 5 cm

2. 17 cm

3. 2 cm

4. 3 cm

Q.

If AB is parallel to CD then $△$ABO should be congruent to $△$CDO always.

Arjun: They will be congruent always.

Rahul: They may or may not be congruent.

Choose the correct option.

1. Arjun is correct

2. Rahul is correct

3. Both of them are correct

4. Both of them are wrong

Q. In the figure, $\text{DA}\perp \text{AB}$, $\text{CB}\perp \text{AB}$ and $\text{AC}=\text{BD}$. State the three pairs of equal parts in $\text{ΔABC}$ and $\text{ΔDAB}$. Which of the following statements is meaningful?
(i) $\text{ΔABC ≅ ΔBAD}$ (ii) $\text{ΔABC ≅ ΔABD}$

Q. QR/QS=QT/PR and angle 1is equal to angle 2. Show that triangle PQS ~ to triangle RTS

Q. In triangle ABC, AB=AC. If the points D, E are on sides AC, AB respectively such that BC=BD and AD=DE=EB, find angle A.

Q.

Triangle ABC is isosceles with AB =BC . If angle B is twice the measure of angle A find the measure of all the angles of the triangle.

Q.

In the given figure, if AB = AC and $\angle ADB=\angle ADC={90}^{\circ }$, then which of the following is true?

1. $△ABD\cong △ADC$ by RHS postulate

2. $△ABD\cong △ADC$ by ASA postulate

3. BD = DC

4. If $\angle ABD={60}^{\circ },then\angle ACD=30°$

Q. In triangle ABC, if the measure of angle A = angle B = 60 degrees, then ABC is ___ triangle.

1. equilateral
2. scalene
3. isosceles
4. right angled

Q. Which congruence criterion is used in the following?
Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$

Q. In the given figure, AD = BC. $\Delta ABC\cong \Delta ADC$ by which of the following criterian?

1. SSS congruency
2. SAS congruency
3. RHS congruency
4. ASA congruency

Q. Briefly, explain congruency of triangles.

Q.

Question 154 (ii)

In the given figure, $QS\perp PR$, $RT\perp PQ$ and QS = RT
Is $\angle PQR=\angle PRQ$? Give reason.

Q.

Question 86

State whether the statement is True or False.

In the given figures, two triangles are congruent by RHS.