AAS Criteria for Congruency

Q. what is the full form of CPCT congruency.and how to solve a sum by CPCT property.

Q. Question 8
If $\Delta ABC$ and $\Delta PQR$ are to be congruent, name one additional pair of corresponding parts.Which criterion did you use?

Q. Question 9
Explain, why
$\Delta ABC\cong \Delta FED$ ?

Q.

If $\Delta ABC\cong \Delta FED$ under the correspondence $ABC\leftrightarrow FED$, write all the corresponding congruent parts of the triangles.

Q.

$△ABC$ is an isosceles triangle with $AB=AC$. Draw $AP\perp BC$ to show that $\angle B=\angle C.$

Q.

In the figure given below, AD and BC are equal and perpendicular to the same line segment AB. CD cuts AB at O. Then the relation between OC and OD is _____ .

1. OD > OC

2. OD < OC

3. $OD$ = $\frac{1}{2}$ $OC$

4. OD = OC

Q.

If $△ABC\cong △PQR$ under the correspondence:

$ABC\leftrightarrow QRP$

Write all the corresponding congruent parts of the triangles.

Q.

For what value of x will $△ABC\cong △XYZ$ ?

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

2. $x={50}^{\circ }$

3. $x={70}^{\circ }$

4. $x={80}^{\circ }$

Q.

Which congruence criterion is used in the following:

Given: $\angle$ MLN = $\angle$ FGH , $\angle$ NML= $\angle$ HFG and LM = HF. So $△$ LMN ≅ $△$ GFH.

1. ASA

2. AAS

3. RHS

4. SAS

Q.

Question 152 (i)

In the given figure, $\angle 1=\angle 2$ and $\angle 3=\angle 4$
Is $\Delta ADC\cong \Delta ABC$? Why?

Q.

If $△ABC\cong △PQR$ under the correspondence:

$ABC\leftrightarrow PQR$

Write all the corresponding congruent parts of the triangles.

Q.

Using the information given in the figure, find the values of x and y.

1. $x=5,y=8$

2. $x=7,y=6$

3. $x=5,y=7$

4. $x=7,y=8$

Q.

In the given figure, if $\angle$ ABC = $\angle$ ADC and $\angle$ BAC = $\angle$ DAC, then by which postulate is $△ABC\cong △ADC$ ?

1. AAS

2. RHS

3. SSS

4. SAS

Q.

In two triangles; if a pair of corresponding angles and a side are equal, then the triangles are necessarily congruent.

1. True

2. False

Q. (a) In the given figure, prove that:


(i) $\Delta ABC\cong \Delta DCB$

(ii) AC = DB

(b) In the figure, it is given that $\angle$A = ${90}^{\circ }$, AB = AC, and D is the mid point of BC. Find $\angle$ADC.

[4 MARKS]

Q.

State whether the following statement is true or false

$\mathrm{AAS}$ congruence criterion is same as $\mathrm{ASA}$ congruence criterion.

1. True
2. False

Q. Angles opposite to equal sides of an isosceles triangle are equal. Prove this result

Q.

If two angles of two triangles are congruent to each other, then the third angles will be congruent to each other.

Using the above statement, choose which two congruency criteria eventually becomes same.

1. SAS and ASA

2. AAS and SAS

3. AAS and ASA

4. No two congruency criteria are same.

Q. In the given figure, prove that: [3 MARKS]



(i) $\Delta ACB\cong \Delta ECD$

(ii) $AB=ED$

Q. In the given figure, if
$\angle B=\angle Y=90°$
XZ = AC and YZ = BC, then the triangles are congruent by RHS criterion.

1. True
2. False

Q. From the given figure it is stated that $AB=AC.$
State true or false.

1. True
2. False

Q.

Question 67

Fill in the blanks to make the statement true.

In the given figure, $\Delta ARO\cong \Delta$ ___

Q.

In the given figure, AB and CD intersect at O. If AC = DB and $\angle ACO=\angle DBO$ then which of the following is true ?

1. $△AOC\cong △DOB$ by AAS postulate

2. $△AOC\cong △DOB$ by SAA postulate

3. AO = DO

4. O is midpoint of CD

Q. What is sad and asa

Q.

If $\Delta PNE\cong \Delta CAR$, If PN = CR then name all the other corresponding parts of $\Delta PEN$ and $\Delta CAR$. [2 MARKS]

Q. If sides AB = QR, BC = RP and AC = QP, then triangle ABC is congruent to triangle _____.

1. PQR
2. QPR
3. QRP
4. RPQ

Q. Which congruence criterion do you use in the following?
Given, AC = DF, AB = DE, BC = EF
So, $\Delta ABC\cong \Delta DEF$

Q.

OX bisects $\angle AOB$. C is any point on OX. if $CD\perp OA$ and $CE\perp OB$, then which of the following is true ?

1. $△COD\cong △COE$ by AAS postulate

2. $△COD\cong △COE$ by RHS postulate

3. $△COD\cong △COE$ by SAA postulate

4. CD = CE

Q. If two triangles have their corresponding angles equal, are they always congruent? If not, draw two triangles which are not congruent but which have their corresponding angles equal.

Q.

Question 66

Fill in the blanks to make the statement true.

In the given figure, $\Delta$ ___ $\cong \Delta PQR$