SAS Criteria for Congruency

Q. What is the difference between SAS and ASS rule of congruency

Q.

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

1. True

2. False

Q.

Name the sides and angles of the following triangles.

Q. Question 3
You have to show that $\Delta AMP\cong \Delta AMQ$. In the following proof, supply the missing reasons:
$\begin{array}{cc}Steps& Reasons\\ i)PM=QM& \left(i\right)\\ ii)\angle PMA=\angle QMA& \left(ii\right)\\ iii)AM=AM& \left(iii\right)\\ iv)\Delta AMP\cong \Delta AMQ& \left(iv\right)\end{array}$

Q.

Question 99

State whether the statement is True or False.

If two legs of a right-angled triangle are equal to two legs of another right-angled triangle, then the right triangles are congruent.

Q.

Which pair of triangles are congruent by $ASA$ ?

1. 

2. 

3. 

4. 

Q.

Question 3
Examine whether you can construct $\Delta$ DEF such that EF = 7.2 cm, $\angle$ E = ${110}^{\circ }$ and $\angle$ F = ${80}^{\circ }$. Justify your answer:

Q.

If triangle ABC is congruent to triangle QPR, then angle A is equal to angle

1. P
2. R
3. Q
4. None

Q.

In the figure given below, name the parts of the triangles that can be used to prove the congruence of the two triangles.

1. ∠B = ∠D; ∠C = ∠E

2. AC = AE; AB = AD; BC = DE

3. AB = AD; BC = DE; ∠B = ∠D

4. ∠B = ∠D; ∠C = ∠E; AB = AD

Q. In the given diagram, equilateral triangle $EAB$ surmounts square $ABCD$. Find the the measure of $\angle AEC$.

1. ${30}^{\circ }$
2. ${15}^{\circ }$
3. ${45}^{\circ }$
4. ${25}^{\circ }$

Q.

There is a park with two triangular jogging tracks. Rahul and his friend Arjun went for jogging and their jogging is completed after they reach their stating point. The park had a route map which mentioned that the sides of jogging tracks with the same color have the same length and nothing was mentioned about different colored sides.

Both of them started jogging at 7 AM on different tracks. Rahul finished his jogging at 7:40 AM. At what time will Arjun finish his jogging if both of them are jogging at the same speed?

1. Before 7:40 AM

2. After 7:40 AM

3. 7:40 AM

4. Cannot be determined because the speed with which the friends were jogging was not given

Q.

In the given figure if AB = AC and AD bisects $\angle BAC$, then which of the following are true ?

1. $△BAD\cong △CAD$ by ASA postulate

2. $△BAD\cong △CAD$ by SAS postulate

3. $AD\perp BC$

4. D is the mid point of BC

Q.

Question 151

In the given figure, DE = IH, EG = FI and $\angle E=\angle I$. Is $\Delta DEF\cong \Delta HIG$? If yes, by which congruence criterion?

Q.

Question 149 (i)

State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).

$\Delta PQR:PQ=3.5cm,$ $QR=4.0cm$, $\angle Q={60}^{\circ }$
$\Delta STU:ST=3.5cm$, $TU=4.0cm$, $\angle T={60}^{\circ }$

Q. In the given figure, state whether $\Delta ABC\cong \Delta EOD$ or not. If yes, state the criterion of congruence.

1. $SAS$
2. $RHS$
3. $SSS$
4. $AAA$

Q.

$△QRS$ is congruent to which of these triangles and what is the congruency condition being fulfilled?

1. $△$ QTP, SAS

2. $△$ PTQ, AAS

3. $△$ TPQ, ASA

4. $△$ TQP, SAS

Q. Construct $\Delta PQR$, given $\angle RPQ={30}^{\circ },\overline{PQ}=4.5cm$, and $\angle PQR={45}^{\circ }$ [4 MARKS]

Q.

If $△ABC$ and $△XYZ$ are right-angled triangles, right angled at B and Y respectively, then for what value of x will $△ABC$ be congruent to $△XYZ$ ?

1. x = 10 cm
2. x = 8 cm
3. x = 6 cm
4. x = 5 cm

Q.

In the given figure, if $AD\perp BC$ and BD = DC, then which of the following are true ?

1. $△BAD\cong △CAD$ by ASA postulate

2. $△BAD\cong △CAD$ SAS postulate

3. AD bisects $\angle$ BAC

4. $△ABC$ is isosceles

Q.

In the given figure, AD = BC. What is the length of AB if DC = 4 cm?

1. 5 cm

2. 4 cm

3. 3 cm

4. Can’t find

Q.

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

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

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

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

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

Q.

In the below quadrilateral ABCD, if AD = BC and $\angle DAB$ = $\angle CBA$, then,

1. ∠ABD = ∠BAC

2. ∠ABD < ∠BAC

3. ∠ABD > ∠BAC

4. ∠DAB =∠BAC

Q.

In the given figure, if AP = BP and DP = CP, then which of the following are true?

1. $△PAD\cong △PBC$ by SAS postulate

2. $△BAD\cong △ABC$ by SSS postulate

3. $△BAD\cong △ABC$ by ASA postulate

4. AP = AB

Q.

In the given figure $\angle BCA$ = $\angle RPQ$ = ${25}^{\circ }$, then find $\angle PQR$.

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

2. ${35}^{\circ }$

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

4. ${25}^{\circ }$

Q.

In triangles ABC and PQR, ∠C = ∠R, BC = QR and ∠B = ∠Q then they are in congruence according to?

1. ASA criteria

2. SAS criteria

3. AAA criteria

4. SSS criteria

Q.

If $△ABC$ and $△XYZ$ are right-angled triangles, right angled at B and Y respectively, then for what value of x will $△ABC$ be congruent to $△XYZ$ ?

1. x = 10 cm
2. x = 8 cm
3. x = 6 cm
4. x = 5 cm

Q.

If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Q.

If $△ABC$ and $△XYZ$ are right-angled triangles, right angled at B and Y respectively, then for what value of x will $△ABC$ be congruent to $△XYZ$ ?

1. x = 8 cm
2. x = 10 cm
3. x = 6 cm
4. x = 5 cm

Q.

In the quadrilateral ABCD, if AD = BC and $\angle DAB$ = $\angle CBA$, then relation between $\angle ABD$ and $\angle BAC$ is

1. ∠ABD = ∠BAC

2. ∠ABD < ∠BAC

3. ∠DAB =∠BAC

4. ∠ABD > ∠BAC

Q.

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°

In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?