ASA Criteria for Congruency

Q. What is the difference between ASA and AAS criterion?

1. In AAS we consider non - included side whereas in ASA we consider included side.
2. In AAS we consider included side whereas in ASA we consider non - included side.
3. In AAS we consider included angle whereas in ASA we consider non - included angle.
4. In AAS we consider non - included angle whereas in ASA we consider included angle.

Q. If$△$ABC is congruent to $△$ DEF where AB = DE and BC = EF, then match the following.

1. DF
2. $\angle$EDF
3. $\angle$DFE

Q. If $△$ABC is congruent to $△$PQR, then the value of $\angle$A is ____.

1. 35°
2. 55°
3. 90°
4. 45°

Q.

Question 104

State whether the statement is True or False.

If the hypotenuse and an acute angle of one right-angled triangle are equal to the hypotenuse and an acute angle of another right-angled triangle, then the triangles are congruent.

Q.

Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

a) RHS congruence criterion
b) ASA congruence criterion
c) SAS congruence criterion
d) AAA congruence criterion

Q. For the given congruent triangles $PQR$ and $STU$ under ASA criterion, find the value of $x$ and $y$.

1. $x={60}^{\circ },y={60}^{\circ }$
2. $x={20}^{\circ },y={100}^{\circ }$
3. $x={90}^{\circ },y={30}^{\circ }$
4. $x={30}^{\circ },y={90}^{\circ }$

Q.

What is the full form if CPCT in congruence of triangles

Q.

Question 153 (i)

Observe the following figure and state the three pairs of equal parts in $\Delta ABC$ and $\Delta DBC$.
Is $\Delta ABC\cong \Delta DCB$? Why?

Q.

Question 152 (ii)

In the given figure, $\angle 1=\angle 2$ and $\angle 3=\angle 4$
Show that AD = AB and CD = CB

Q.

Question 2 (c)
You want to show that$\Delta ART\cong \Delta PEN$:
If it is given that AT = PN and you are to use ASA criterion, you need to have:
i) ? (ii)?

Q. In given figure, can you use ASA congruence rule and conclude that $\text{ΔAOC ≅ ΔBOD}$?

Q. Line segments ab and cd bisect each other at o.ac and bd are joined forming triangles aoc and bod.state three equality relations between the parts of the two triangles, that are given or otherwise known. Are the two triangles are congruent. State in symbolic form . Which congruence do you use

Q.

If $\mathrm{AB}=\mathrm{QR},\mathrm{BC}=\mathrm{PR}$and $\mathrm{CA}=\mathrm{PQ}$, then

1. $\Delta ABC\cong \Delta PQR$

2. $\Delta CBA\cong \Delta PRQ$

3. $\Delta BAC\cong \Delta RPQ$

4. $\Delta PQR\cong \Delta BCA$

Q. If $\Delta$ ABC and $\Delta$ PQR are congruent, find the side congruent to AC.

1. QR
2. PR
3. PQ
4. QP

Q. Match the following pairs of triangles with their corresponding congruency criteria.

1. SAS criterion
2. ASA criterion
3. SSS criterion

Q. If $\Delta ABC$ and $\Delta PQR$ are to be congruent, name one additional pair of corresponding parts. Which criterion did you use?

Q.

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

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

Q. If △ABC and △PQR are to be congruent with ∠B = ∠Q and ∠C = ∠R, name one additional pair of corresponding parts

1. BC=QR
2. BC=PQ
3. BC=PR
4. AC=PR

Q. Identify the rule of congruency illustrated by which the two triangles are congruent.

Q.

Consider the figure below:

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

___

Q.

In the figure given below, if $BC=QR,AB=PRandAC=PQ$ then the correct statement is

1. $△ABC\cong △PQR$

2. $△ABC\cong △PRQ$

3. $△ABC\cong △RPQ$

4. $△ABC\cong △RQP$

Q.

In the given figure, P is the midpoint of AB. If $\angle PAC=\angle PBD,$ then which of the following are true ?

1. $△APC\cong △BPD$ by SAS postulate

2. $△APC\cong △BPD$ by SSS postulate

3. $△APC\cong △BPD$ ASA postulate

4. P is midpoint of CD

Q. A carom board $(4cm\times 4cm)$ has the queen at the centre. When the queen is hit by the striker, it moves to the front edge, rebounds and goes into the hole behind the striking line. The displacement of the queen is .

1. 20cm
2. $\frac{2\sqrt{10}}{3}$cm
3. $20\sqrt{2}cm$
4. $40\sqrt{2}cm$

Q. In triangles ABC and PQR, ∠A = ∠P, AB = PQ and ∠B = ∠Q; then by which congruency criterion are these two triangles congruent?

Q. In triangles ABC and PQR, ∠A = ∠P, AB = PQ and ∠B = ∠Q; then by which congruency criterion are these two triangles congruent?

1. ASA criterion
2. SAS criterion
3. SSS criterion
4. AAA criterion

Q.

Question 148 (i)

In the given figure, verify whether given pair of triangles is congruent by SAS congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.

Q.

In the given figure, P is the midpoint of AB. If $\angle PAC=\angle PBD,$ then which of the following are true ?

1. $△APC\cong △BPD$ by SAS postulate

2. $△APC\cong △BPD$ by SSS postulate

3. $△APC\cong △BPD$ ASA postulate

4. P is midpoint of CD

Q.

In two triangles, if a pair of corresponding angles and the side included between the angles are equal, then the triangles are congruent by ___.

1. ASA criterion

2. RHS criterion

3. SAS criterion

4. SSS criterion

Q. In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. Find, x + y.

1. 12
2. 14
3. 10
4. 11

Q. Can the following triangles exist? [3 MARKS]
(i) AB = 8 cm, BC = 6 cm, AC = 10cm
(ii) MN = 9 cm, NO = 5 cm, OM = 4 cm
(iii) $\angle A$ = ${175}^{\circ }$, $\angle B$ = $5^{\circ }$ and $\angle C$ = $0^{\circ }$