SAS Rule

Q.

In the figure given below, find z.

1. ${40}^{\circ }$
2. ${110}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q.

Using the information given in the figure, the values of x and y are __

1. $x=15,y={60}^{\circ }$

2. $x=15,y={30}^{\circ }$

3. $x=30,y={30}^{\circ }$

4. $x=10,y={60}^{\circ }$

Q. In the figure given below, $\angle DAB={100}^{\circ }and\angle DBC={30}^{\circ }$. Find$\angle BDC$.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${100}^{\circ }$
4. ${50}^{\circ }$

Q.

Prove that $△$AOD $\cong$ $△$BOC.

Q.

In the figure below, $△$ABC $\cong$ $△$BED, $\angle$DEB = ${115}^{\circ }$ and $\angle$CAB = ${25}^{\circ }$. It can be concluded that

1. BC || ED
2. $\angle CBD={40}^{\circ }$
3. $\angle CBD={90}^{\circ }$
4. $\angle BDE={60}^{\circ }$

Q.

If one of the angles of a triangle is ${130}^{\circ }$, then the angle between the bisectors of the other two angles can be

1. ${50}^{\circ }$
2. ${65}^{\circ }$
3. ${145}^{\circ }$
4. ${155}^{\circ }$

Q.

In the following figure, $△ABC\cong △ACD$ if ___.

1. BC = AC

2. BC = AD

3. BC = CD

4. CD = AC

Q. Which of the following is correct regarding the figure given below?

1. BC < AC < CD
2. AC < BC < CD
3. AC < CD < BC
4. CD < AC < BC

Q. If 1 side and 1 angle of a triangle are equal to 1 side and 1 angle of another triangle, then they are said to be congruent.

1. False
2. True

Q.

In the given figure, if OA = BO and OC = OD, then, $\Delta AOD$ $\cong$ $\Delta BOC$ by __ congruence rule.

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

Q.

In the following figure, $△ABC\cong △ACD$ if ___.

1. BC = AC

2. BC = AD

3. BC = CD

4. CD = AC

Q. In the figure, $A,B,C$ and $D$ are four points on a circle. $AC$ and $BD$ intersect at a point $E$, such that $\angle BEC={130}^o$ and $\angle ECD={20}^o$. Find $\angle BAC$.

Q. In an isosceles triangle $AB=AC$ and $\angle B={65}^o.$ Which is the shortest side?

Q. If 1 side and 1 angle of a triangle are equal to 1 side and 1 angle of another triangle, then they are said to be congruent.

1. False
2. True

Q.

In the figure, $△ABC$ is an isosceles triangle in which AB = AC. If D and E are the mid-points of sides AB and AC respectively and $\angle DOE={120}^{\circ }$, then find $\angle ODE$.

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${75}^{\circ }$

Q. In the figure, $ABCD$ is a parallelogram in which $\angle BAO={35}^o,\angle DAO={40}^o$ and $\angle COD={105}^o$. Calculate $\angle ACB$

Q.

In the following figure, $△ABC\cong △ACD$ if ___.

1. BC = AC

2. BC = AD

3. BC = CD

4. CD = AC

Q.

$\text{In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of}\Delta ABC\text{such that AX = AY. Prove that CX = BY.}$

(2 Marks)

Q. Both these triangles are congruent by SAS.

1. True
2. False

Q. If 2 sides and the included angle of a triangle are equal to 2 sides and the included angle of another triangle, then they are congruent.

1. False
2. True

Q.

In the given figure, if OA = BO and OC = OD, then, $\Delta AOD\cong \Delta BOC$ by SAS congruence rule.

1. False
2. True

Q. In the given figures, $PQRS$ is a parallelogram .Find the value of $x,y$ and $z$.

Q.

In the given figure, if $\angle$ACB = ${30}^{\circ }$, then what is the value of $\angle$ACD?

Q. Let $ABC$ be an acute-angled triangle; $AD$ be the bisector of $\angle$ $BAC$ with $D$ on $BC$; and $BE$ be the altitude from $B$ on $AC$. Find $\angle$ $CED$

1. $>45$ ${}^{\circ }$
2. $<45$ ${}^{\circ }$
3. $=30$ ${}^{\circ }$
4. None

Q. Suppose in a quadeilateral ABCD, it is given that $AB=AD$ and $\angle ABC=\angle ADC$. Prove that ABCD is a kite.

Q. In two triangles, if two corresponding sides and the included angle are equal, then they are congruent by ___.

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

Q.

In the given $AD=BE$ and $\angle DAB=\angle EBA$. Which of the following statements are true?

1. $\Delta DAB\cong \Delta EBA$ by SAS postulate

2. $\Delta DAB\cong \Delta EBA$ by ASA postulate

3. $\Delta DAB\cong \Delta EBA$ by AAS postulate

4. $BD=AE$