ASA Congruency

Q. In given figure, lIIm and line segments AB, CD and EF are concurrent at point P. Prove that
$\frac{AE}{BF}=\frac{AC}{BD}=\frac{CE}{FD}$

Q. In figure, line segments AB and CD bisect each other at O. Identify the triangles which are congruent.

Q. In the given figure, AC = CE and $AB\parallel ED$. The value of $x$ is ___ units.

1. 10 units
2. 15 units
3. 20 units
4. 25 units

Q.

In the below figure, $\Delta AEC$ and $\Delta DBF$ are equilateral. Prove that all other triangles are equilateral. (Given that bases of the triangles are parallel).
[4 MARKS]

Q. In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.

Q.

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

1. SSS

2. SAS

3. ASA

4. RHS

Q. DF is equal to QR and $\angle$Q equals $\angle$D. Which is the closest criterion for congruency of triangles to prove the given two triangles are congruent?

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

Q. In the given figure, if $\angle x=\angle y$ and AB = CB, then AE is _____.

1. less than CD
2. greater than CD
3. equal to CD
4. data insufficient

Q. In the given figure, if AD = BC and AB || CD then which of the following is true?

1. AB = DC
2. None.
3. AB = AD
4. BC = CD

Q.

If in $△ABC$, $AB=10cm$, $\angle CAB$ = ${30}^{\circ }$ and $\angle CBA$ = ${60}^{\circ }$ and in $△DEF$, $FE=10cm$, $\angle DFE={30}^{\circ }$, $\angle DEF={60}^{\circ }$; then, select the correct statement.

1. ΔBCA $\cong$ ΔEFD

2. ΔBAC $\cong$ ΔFDE

3. ΔABC $\cong$ ΔFDE

4. ΔABC $\cong$ ΔFED

Q. Which criteria for congruency of triangles can be used to prove the given two triangles are congruent?

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

Q.

Consider the figure and choose the correct option.

1. $\Delta ABC\cong \Delta DEF$

2. $\Delta ABC\cong \Delta DFE$

3. $\Delta ABC\cong \Delta FED$​

4. $\Delta ABC$ $≆$ $\Delta FED$​

Q. What does "A.S.A." stand for in congruence criteria?

1. Angle-Side-Angle
2. Add-Single-Angle
3. Add-Subtract-Add
4. Add-Side-Angle

Q.
In the given figure, AC = CE and $AB\parallel ED$. The value of $x$ is ___ units.

Q. In the given figure, $AB=AC$ and $\angle GBC=\angle HCB={90}^{\circ }$.
Which of the following statements is true?

1. BG = CB and AG = AH
2. AG = AB and BG = CH
3. BG = CH and AG = AH
4. $\angle BAC={120}^{\circ }$

Q.

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

1. SAS

2. SSS

3. ASA

4. RHS