# SAS Criteria for Congruency

## Trending Questions

**Q.**

Prove that angles opposite to equal sides of an isosceles triangle are equal.

**Q.**

AD is an altitude of an isosceles ΔABC in which AB = AC.Show that (i) AD bisects BC, (ii) AD bisects ∠A.

**Q.**

In ΔABC and ΔDEF, it is given that AB = DE and BC = EF. In order that ΔABC≅ ΔDEF, we must have(a) ∠A=∠D (b) ∠B=∠E (c) ∠C=∠F (d) none of these

**Q.**

Show that the diagonals of a square are equal and bisect each other at right angles.

**Q.**

In the figure, ABC is a triangle in which ∠B=2∠C. D is a point on side BC such that AD bisects ∠BAC and AB=CD. BE is the bisector of ∠B. The measure of ∠BAC is

72∘

73∘

74∘

95∘

**Q.**If two isosceles triangles have a common base, then prove that the line joining their vertices bisects them at right angles.

**Q.**

If √m + √n - √p = 0 then find value of (m+n-p)^2.

**Q.**

$AD$ and$BC$ are equal perpendiculars to a line segment $AB$ (see Fig.) . Show that $CD$ bisects $AB$.

**Q.**

If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then, the two triangles are congruent by

**Q.**

In a triangle ABC, D is mid-point of BC; AD is produced upto E so that DE = AD. Prove that :

(i) Δ ABD and Δ ECD are congruent.

(ii) AB = EC.

(iii) AB is parallel to EC.

**Q.**

"If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent." Is the statement true? Why?

**Q.**

$O$ is a point in the interior of a square $ABCD$ such that triangle $\u25b3OAB$ is an equilateral triangle. Show that $\u2206OCD$ is an isosceles triangle.

**Q.**

In an isosceles triangle ABC with AB=AC, D and E are points on BC such that BE=CD. The value of ADAE is equal to

1

2

3

4

**Q.**

In the following diagrams, ABCD is a square and APB is an equilateral triangle.

In each case,

(i) Prove that : Δ APD ≅Δ BPC

(ii) Find the angles of Δ DPC.

**Q.**

In the figure, PQRS is a square and SRT is an equilateral triangle. Prove that

(i) PT = QT (ii) ∠TQR=15∘

**Q.**

**Question 1**

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

**Q.**

In the given figure, O is a point in the interior of square ABCD such that ΔOAB is an equilateral triangle.Show that ΔOCD is an isosceles triangle.

**Q.**

The line segments joining the midpoints M and N of parallel sides AB and DC respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD = BC.

**Q.**

On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn.

Prove that: (i) ∠ CAD = ∠ BAE

(ii) CD = BE.

**Q.**

In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP= BQ = CR. Prove that triangle PQR is equilateral.

**Q.**

A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that : QA =QB.

**Q.**

In a Δ ABC, BD is the median to the side AC, BD is produced to E such that BD = DE.

Prove that : AE is parallel to BC.

**Q.**

CDE is an equilateral triangle formed on a side a CD of a square ABCD. Show that ΔADE≅ ΔBCE.

**Q.**

If two sides and the included angle of a triangle are respectively equal to two sides and the included angle of another triangle, the two triangles are congruent. State True or False.

True

False

**Q.**Triangle formed by joining the mid-points of the sides of an isosceles triangle is always a/an

- Scalene triangle
- Equilateral triangle
- Right-angled triangle
- Isosceles triangle

**Q.**

In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY. Prove that CX = BY.

**Q.**

In the figure, it is given that RT = TS, ∠1=2 ∠2 and ∠4=2 ∠3. Prove that ΔRBT≅SAT.

**Q.**In the given figure, ABCD is a quadrilateral, AB = 9 cm, BC = 12 cm, CD = 13 cm, ED = 5 cm and AC = 15 cm. Perpendiculars are drawn from B and D to AC, meeting AC at points P and Q respectively. Which of the following is correct?

- ΔABC ≅ ΔADC
- ΔABC ≅ ΔAEC
- ΔAEC ≅ ΔCDE
- ΔABE ≅ ΔCQD

**Q.**Question 2

In figure, D and E are points on side BC of the a ΔABC such that BD = CE and AD = AE, show that ΔABD≅ΔAE show that ΔABD≅ΔACE

**Q.**

The perpendicular bisectors of the sides of a triangle ABC meet at I.

Prove that : IA = IB = IC.