# ASA Criteria for Congruency

## Trending Questions

**Q.**

If two angles and the included side of a triangle are equal to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

ASA

AAA

SAS

RHS

**Q.**

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

**Q.**

Prove that the centre of the circum circle of a right angled triangle is the midpoint of its hypotenuse.

**Q.**In triangles ABC and PQR, ∠C = ∠R, BC = QR and ∠B = ∠Q, then by which congruency criteria are these two triangles congruent?

- A.S.A. criterion
- S.A.S. criterion
- A.A.A. criterion
- S.S.S. criterion

**Q.**40. Triangle PQR is a right triangle which is right angled at Q. QX perpendicular to PR, XY perpendicular to RQ and XZ perpendicular to PQ are drawn. Prove that ZX2=PZ x ZQ

**Q.**Question 7

P and Q are the mid – points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

**Q.**

In ∆ABC and ∆DEF, AB = DF and ∠A = ∠D. The two triangles will be congruent by SAS axiom if:

BC = DE

AC = EF

BC = EF

AC = DE

**Q.**

In the figure given below, $PQR$is an isosceles triangle in which $PQ=PR$, $PQ$and $PR$are produced to $S$and $T$respectively such that $QS=RT$. Show that $RS=QT$

**Q.**

ABCD is a quadrilateral such that diagonal AC bisects that angles ∠A and ∠C. Prove that AB = AD and CB = CD.

**Q.**

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

(i) ΔABD ≅ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

**Q.**

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB=AC. Prove that BD = CE.

**Q.**

In the adjoining figure, the side AC of ∆ABC is produced to E such that CE = 1/2 AC. If D is the midpoint of BC and ED produced meets AB at F, and CP, DQ are drawn parallel to BA, then FD is

FD = 1/3 FE

FD = 2/3 FE

FD = 1/2 FE

FD = 1/4 FE

**Q.**

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

**Q.**

In ΔABC and ΔDEF , it is given that ∠B=∠E and ∠C=∠F. In order that ΔABC≅ ΔDEF, we must have(a) AB=DF (b) AC=DE (c) BC=EF (d) ∠A=∠D

**Q.**

For what value of x will △ABC be congruent to △XYZ ?

- x=50∘
- x=40∘
- x=60∘
- x=30∘

**Q.**

Prove that the four triangles got by joining the midpoints of a triangle are all congruent and that they are similar to the original triangle.

**Q.**In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:

(a) SAS

(b) ASA

(c) SSS

(d) RHS

**Q.**In the adjacent figure, △ ABC, D is the midpoint of BC. DE⊥ AB, DF⊥ AC and DE = DF. Show that △ BED ≅△ CFD

**Q.**

In triangles $\mathrm{ABC}$ and $\mathrm{PQR}$, $\angle \mathrm{A}=\angle \mathrm{Q}$ and $\angle \mathrm{B}=\angle \mathrm{R}$.

Which side of $\u25b3\mathrm{PQR}$ should be equal to side $\mathrm{BC}$ of $\u25b3\mathrm{ABC}$ so that the two triangles are congruent.

**Q.**

$\u25b3ABC$ is an isosceles triangle in which $AC=BC$. $AD$ and$BE$ are respectively two altitudes to sides $BC$ and $AC$. Prove that $AE=BD$.

**Q.**

In the adjoining figure, explain how one can find the breadth of the river without crossing it.

**Q.**

In the given figure, two parallel lines l and m are intersected by two parallel lines p and q.

Show that ΔABC≅ΔCDA.

**Q.**ABCD is a quadrilateral such that AB=AD and CB=CD.Prove that AC is the perpendicular bisector of BD.

**Q.**If CE is parallel to DB in the given figure, then the value of ‘x’ is 30∘ .

- True
- False

**Q.**In a triangle ABC, if AD is the bisector of ∠BAC, which meets BC at point D such that AD ⊥ BC, then which of the following is always true?

- BC = AC
- BD = AD
- ΔABD ≅ ΔCAD
- ∠ABD = ∠ACD

**Q.**

In the given figure, BE and CF are two equal altitudes of ΔABC.Show that (i) ΔABE≅ ΔACF, (ii) AB=AC.

**Q.**

In triangles ABC and PQR, if ∠A=∠R.

∠B=∠P and AB=RP, then which one of the following congruence condition applies:

ASA

SSS

SAS

RHS

**Q.**

If in △ABC, AB=10 cm, ∠CAB = 30∘ and ∠CBA = 60∘ and in △DEF, FE=10 cm, ∠DFE=30∘, ∠DEF=60∘; then, select the correct statement.

ΔBAC ≅ ΔFDE

ΔBCA ≅ ΔEFD

ΔABC ≅ ΔFDE

ΔABC ≅ ΔFED

**Q.**

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Prove that :

(i) Δ DCE ≅Δ LBE

(ii) AB = BL.

(iii) AL = 2DC

**Q.**Prove that two triangles are congruent if any two sides and the

included angle of one triangle is equal to any two sides and the included angle of other triangle.