SAS Congruency Postulate

Q. Question 3
‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, than the two triangles must be congruent’. Is the statement true? Why?

Q.

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

1. True

2. False

Q.

In the given figure, $AB$ and $CD$ bisect each other at $O$, and $AD=BC$.

(i) State the three pairs of equal parts in $∆OAD$ and $∆OBC$.

(ii) Is $∆AOD\cong ∆BOC$? Why or why not?

(iii) Is $AD\parallel CB$? Why?

Q.

Which congruence criterion is used in the following?

Given: $\angle MLN=\angle FGH,\angle NML=\angle HFG,ML=FG$
So, $\Delta LMN\cong \Delta GFH$

Q.

Question 1 (b)\angle{F}
Which congruence criterion do you use in the following?

Given: RP = ZX, RQ = ZY, $\angle PRQ=\angle XZY$
So, $\Delta PQR\cong \Delta XY$

Q.

It is given that $\Delta ABC\cong \Delta RPQ$. Is it true to say that $BC=QR$ ? Why?

1. True
2. False

Q.

Consider the figure below:

If $\Delta BOC\cong \Delta AOD$ , and $\angle$ $ADO={30}^o$, then what is the measure of $\angle BCO$ (in degrees) ?

___

Q. Which congruence criterion is used in the following?
Given: $\angle MLN=\angle FGH,\angle NML=\angle HFG,ML=FG$
So $\Delta LMN\cong \Delta GFH$ [2 MARKS]

Q.

In the given figure, if $\angle BCA=\angle RPQ={15}^{\circ },$
then $\angle PQR$ is ______.

1. ${45}^{\circ }$

2. ${15}^{\circ }$

3. ${55}^{\circ }$

4. ${35}^{\circ }$

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 x = y and AB = CB, then AE is _____.

1. greater than CD

2. equal to CD

3. less than CD

4. Can't be determined

Q.

If in the given figure, ABCD is a rectangle and DCE is an equilateral triangle, then which of the following statements is/are correct?

1. $\Delta DAE\cong \Delta CBE$
2. $\angle DAE={15}^{\circ }$
3. $\Delta AEB$ is isosceles.
4. $\Delta DAE$ is isosceles.

Q.

$\text{In the given figure,}\Delta ABC\text{and}\Delta OBC\text{are both isosceles with base BC}$
$\text{It can be concluded that:}$

1. $\Delta AOB\cong \Delta AOC$

2. RHS rule is applied

3. SSS rule is applied

4. $\Delta AOB\text{is not congruent to}\Delta AOC$

Q.

$△ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. $\angle BCD$ is equal to ____.

1. ${90}^{\circ }$

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

3. Cannot be determined

4. ${37}^{\circ }$

Q.

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

Q. Both these triangles are congruent by SAS.

1. True
2. False

Q.

In the following figure, if AC = BE, then AD = ___.

1. BD

2. AE

3. CE

4. None of the above

Q.

In the given figure $AB=DC$, $\angle ABC=\angle DCB$. Prove that

(i) $∆ABC\cong ∆DCB$

(ii) $\angle A=\angle D$

(iii) $AC=DB$

Q.

From adjacent figure, we can conclude that $∆ABC\cong ∆ADC$

1. True
2. False

Q.

Given below are the measurements of some parts of two triangles. Examine whether the two triangles or not by using SAS congruence rule. If the triangles are congruent, write them in symbolic form.

$$\begin{gathered} △ABC△DEF \\ AB=4.5cm,AC=4cm,\angle A=60°DE=4cm,FD=4.5cm,\angle D=55° \end{gathered}$$

Q.

In triangles$\mathrm{ABC}\mathrm{and}\mathrm{PQR},\mathrm{if}\angle \mathrm{A}=\angle \mathrm{R},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{AB}=\mathrm{RP},$then which one of the following congruence condition applies:

1. SAS

2. SSS

3. ASA

4. RHS

Q. In the given parallelogram ABCD, DP = BQ and $\angle ADP=\angle CBQ$. To which triangle is $\Delta ADP$ congruent to?

1. $\Delta CBQ$
2. $\Delta PDQ$
3. $\Delta PQB$
4. $\Delta QBC$

Q.

In triangles $ABCandPQR$, three equality relations between some parts are as follows:

$\mathrm{AB}=\mathrm{QP},\angle \mathrm{B}=\angle \mathrm{P}\mathrm{and}\mathrm{BC}=\mathrm{PR}$

State which of the congruence conditions applies:

1. SAS

2. SSS

3. ASA

4. RHS