SSS Postulate

Q.

An exterior angle of a triangle is 120° and one of the interior opposite angles is 30°. Find the other angles of the triangle.

Q. In triangle ABC, AB = AC and angle B = 40o${\mathrm{.}}^{}$What is the value of ∠C?

1. ∠C = 90o
2. ∠C = 40o
3. ∠C = 80o
4. ∠C = 70o

Q.

In each of the following figure, find the value of x:

Q.

Find $x$ in the following figure:

Q.

If the exterior angles of a triangle are in the ratio $4:5:6,$ find the ratio of the angles of the triangle.

Q.

In the given figure $ABCD$ is a square. Find the measure of $\angle CAD$.

Q. In a $\Delta PQR,$ $P{R}^2-P{Q}^2=Q{R}^2$ and M is a point on side PR such that $QM\perp PR$. Prove that $Q{M}^2=PM\times MR$

Q. If in two triangles ABC and PQR , AB = PQ, AC = PR and BC = QR then which of the following is correct?

1. $\Delta$ABC ≅ $\Delta$PQR
2. $\Delta$ABC = $\Delta$PRQ
3. $\Delta$BCA ≅ $\Delta$RQP
4. $\Delta$BCA = $\Delta$RQP

Q.

Sides BC, CA and AB of a triangle ABC are produced in an order, forming exterior angles ∠ACD, ∠BAE and ∠CBF. Show that ∠ACD + ∠BAE + ∠CBF = 360°.

Q.

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

1. $△ABC\cong △ADC$ by SAS postulate

2. If $\angle ABC=x^{\circ }$, then $\angle ADC=x^{\circ }$

3. If $\angle BAC=y^{\circ },$ then $\angle DCA=y^{\circ }$

4. $△ABC\cong △ADC$ by SSS postulate

Q.

The three sides of a triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent by which condition?

1. SAS

2. ASA

3. SSS

4. RHS

Q.

In $△ABC$ and $△XZY$, if AB = XZ, BC = ZY and CA = YX, then by which postulate is $△ABC$ congruent to $△XZY$ ?

1. SSS

2. SAS

3. ASA

4. RHS

Q.

In $△PQR$ and $△XZY$, if PQ = XZ, QR = ZY and RP = YX, then by which postulate is $△PQR\cong △XZY$ ?

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

Q.

If all sides of one triangle are correspondingly equal to the sides of other triangle, then the triangles are congruent. True/False?

1. False

2. True

Q.

In the given figure, AC = AD and BC = BD. Which of the following statements are correct?

1. $\Delta ABC\cong \Delta ABD$ by SSS postulate

2. $\Delta ABC\cong \Delta ABD$ by SAS postulate

3. $\angle ACB=\angle ADB$

4. AB bisects $\angle CAD$

Q. If in the following figure, AC = CD, AD = BD and ∠C = ${52}^o$, then the measure of ∠DAB is:

1. ${30}^o$
2. ${32}^o$
3. ${34}^o$
4. ${36}^o$

Q.

Two interior angles in a triangle are 35° and 40°. Find its corresponding exterior angle.

1. 5°

2. 75°

3. 15°

4. 55°

Q.

If AB is perpendicular bisector of CD at P then

1. CD = BD

2. CP = PD

3. AP = PB

4. AC = AD

Q. Find the measure of y in the given figure.

1. 30

Q.

The exterior angles obtained on producing the base of a triangle both ways are 104° and 136°. Find the angles of the triangle.

Q.

In the given figure, if AB = CD and BC = DA, then which of the following is true?

1. $△ABC\cong △CDA$ by SSS postulate

2. $△ABC\cong △CDA$ by SSS postulate

3. AB // CD

4. BC // AD

Q. In the given figure, if ∠BCA = ∠RPQ = ${15}^o$, then ∠PQR is ___.

1. ∠PQR = ${35}^o$
2. ∠PQR = ${15}^o$
3. ∠PQR = ${45}^o$
4. ∠PQR =${25}^o$

Q.

Fill up the blanks to make the following statements true:

(a) Sum of the angles of triangle is ___________.

(b) An exterior angle of a triangle is equal to the sum of ___________ opposite angles.

(c) An exterior angle of a triangle is always ___________ than either of the interior opposite angles.

(d) A triangle cannot have more than ___________ right angle.

(e) A triangle cannot have more than ___________ obtuse angle.

Q. In the given figure, prove that: [2 MARKS]

$\Delta ABD\cong \Delta ACD$

Q. In the figure, if AB = DC and ∠ABO = ${35}^o$. What is the value of ∠DCO?

1. ${25}^o$
2. ${35}^o$
3. ${50}^o$
4. ${70}^o$

Q.

Choose the correct answer from the given alternative:

Sum of the three exterior angles of a triangle is _____________.

A. two right angles

B. three right angles

C. one right angle

D. four right angles

Q. If D is any point on the side BC of $\Delta ABC$ such that $\Delta ADB$ and $\Delta ADC$ are equal in area, then

1. AD is the median
2. AD is the altitude
3. AD is an angle bisector
4. AD is any line

Q.

In the adjacent rectangle ABCD, ∠OCD = 30°. Calculate ∠BOC. What type of triangle is BOC?

Q.

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

1. $x=56°,y={76}^{\circ }$

2. $x={48}^{\circ },y={56}^{\circ }$

3. $x={48}^{\circ },y={76}^{\circ }$

4. $x={76}^{\circ },y={56}^{\circ }$

Q. From the information shown in the figure, state the test assuring the congruence of $△ABC$ and $△PQR$. Write the remaining congruent parts of the triangles.