SAS Criteria for Congruency of Triangles

Q.

Which is the included angle between the sides $DE$ and $EF$ of $\angle DEF$?

1. $\angle E$
2. $\angle F$
3. None of the above
4. $\angle D$

Q. Can two right angles be called adjacent angles?

Q. If $△ABC=△PQR$, then ∠A corresponds to:

1. $\angle P$
2. $\angle R$
3. $\angle Q$
4. None of the above

Q.

In two triangles, if two corresponding sides and an angle are equal, then the triangles are necessarily congruent. True/False?

1. True

2. False

Q.

BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

1. ∠ADB ≅ ∠CDB

2. AD ≅ CD

3. ΔABD ≅ ΔCBD

4. BD ≅ DC

Q. In the given figure, if $\angle BAD=\angle CAD$, $\angle ABD=\angle ACD$ , then which of the following is false?

1. $\Delta ABD\cong \Delta ACD$ by SAS
2. $BD=CD$
3. $\Delta ABD\cong \Delta ACD$ by AAS
4. $AB=CD$

Q.

In $△$ ABC and $△$ XYZ, if AB = XY, BC = YZ and $\angle$ ABC = $\angle$XYZ = ${90}^{\circ }$, then by which postulate is $△ABC$ $\cong △XYZ$ ?

1. SSS

2. SAS

3. ASA

4. RHS

Q.

In the given figure, AP = BP and CP = DP. Which of the following statements are true?

1. $\Delta APC\cong \Delta BPD$ by ASA postulate
2. $\Delta APC\cong \Delta BPD$ by SAS postulate
3. $\angle CAP=\angle DBP$
4. $AC\parallel BD$

Q. In the given figure, if OA = OB and OC = OD, then $△AOD\cong △BOC$ by ____ criterion of congruency.

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

Q. Find $\angle A$ in the figure given below.

1. 60°
2. 50°
3. 80°
4. 70°

Q. examine whether triangeDEF and trianglePQR are congruent or not by ASA congruence rule.
in triangleDEF angleE=80degrees, angleF=30 degrees, EF=5cm
in trianglePQR angleP=80degrees, PQ=5cm, angleR=30degrees.

Q.
Which of the following statement(s) is/are correct for the above two triangles?

1. $\text{CA = QR}$
2. $\angle CAB=\angle QRP$
3. $△BCA\cong △PQR$
4. $\angle CAB=\angle QPR$

Q. Which side of $△$ABC corresponds to side EF of $△$DEF?

1. AB
2. BC
3. CA
4. Cannot say

Q.

What is the criterion of SAS and ASA congruency? [2 MARKS]

Q. In the given figure, AC and DB are perpendicular bisector of each other and AC = DB. Then

1. $△$AOB $\cong$ $△$BOC $\cong$ $△$COD $\cong$ $△$DOA
2. $△$AOB $\cong$ $△$BOC $≆$ $△$COD $\cong$ $△$DOA
3. $△$AOB $\cong$ $△$BOC $\cong$ $△$COD $≆$ $△$DOA
4. $△$AOB $\cong$ $△$BOC $≆$ $△$COD $≆$ $△$DOA

Q. In $△ABC$ and $△PQR$, $\angle A=\angle Q$ and $\angle B=\angle R.$ Which side of $△PQR$ should be equal to side $BC$ of $△ABC$ so that the two triangles are congruent?

1. $QR$
2. $PQ$
3. $RP$
4. Any side of $△PQR$

Q.

(a) In the given figure, prove that $lx\parallel my\parallel nz$. [3 MARKS]

(b) If $k={50}^{\circ }$, then what is the value of $\angle PSY$?

Q. Find the value of 'x' and 'y' respectively if ΔBAC ≅ ΔQRP

1. 15° and 14
2. 25° and 14
3. 14° and 15
4. 14° and 25

Q.
$△$COB is an equilateral triangle and OD=OA.
Which of these statement is correct?

1. AB = DB
2. OC = DO
3. AB = DC
4. DB = AB

Q. In the figure, the two triangles are congruent. The corresponding parts are marked. Complete the congruent statement $\Delta RAT\cong$ ?

Q. If FA = DA and line AE is an angle bisector of angle A, then
$△AEF\cong △AED$ by criteria.

1. SAS
2. RHS
3. ASA

Q.
If, side DE of $△$DEF is equal to side BA of $△$BAC. Then,

1. $△$BAC $\cong △$DEF by ASA criteria
2. $△$BAC $\cong △$DEF by SAS criteria
3. $△$BAC $\cong △$DEF by RHS criteria
4. $△$BAC $\cong △$DEF by SSS criteria

Q.

If two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle, then the triangles are congruent by ____.

1. SSS congruence condition

2. ASA congruence condition

3. RHS congruence condition

4. SAS congruence condition

Q. In $△ABC$ and $△DEF,\angle B\cong \angle F,\angle F=\angle C$ and $AB=3DE$ then which of the statements regarding to two triangle is ture?

1. The triangles are not congruent and not similar
2. The triangles are similar but not congruent
3. The triangles are congruent and similar.
4. None of the statement above is true.

Q. In the figure, the two triangles are congruent. The corresponding parts are marked. Complete the congruent statement $\Delta RAT\cong$ ?

Q.
PQRSTU is a hexagon with all sides equal. Which of these statements is/are correct?

1. UQ = TR
2. UQ = ST
3. $△$PUQ$\cong$$△$STR
4. TR = PU

Q. If there is an equilateral triangle then it is equiangular also having all the three angles equal to

Q. If PR = AB , QR = BC and $\angle R=\angle B$,
then $△ABC\cong △PQR$ by SSA criterion.

1. True
2. False

Q. In the given figure, $AB=AC$, then $DP=DQ$.

1. True
2. False

Q. If $\angle AMQ$ = $\angle AMP={100}^{\circ }$ and $\angle Q={50}^{\circ }$, find the measure of $\angle PAM$.

1. 60${}^{\circ }$
2. 50${}^{\circ }$
3. 30${}^{\circ }$
4. 40${}^{\circ }$