# SAS Postulate

## Trending Questions

**Q.**In figure, line segment DF intersects the side AC of a ΔABC at the point E such that E is the mid – point of CA and ∠AEF and ∠AFE. Prove that BDCD=BFCE

**Q.**

If two triangles are congruent, the number of pairs of corresponding parts is

**Q.**

Prove that if one pair of opposite sides of a quadrilateral are equal and parallel, then it is a parallelogram.

**Q.**Prove that opposite sides and angles of a parallelogram are equal

**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 ____ congruence condition.

- SSA
- SSS
- RHS
- SAS

**Q.**

Prove that a ΔABC is an isosceles triangle if the altitude AD from A on BC bisects BC.

**Q.**

In figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the midpoint of line segment AB as well as PQ.

**Q.**

In the given figure, If AB || DC and P is the midpoint of BD. Prove that P is also the midpoint of AC.

**Q.**Question 2 (i)

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

ΔABD≅ΔBAC

**Q.**

A triangle can be drawn if two sides and _____ angle are given.

included

any

no

not sure

**Q.**If, in two triangles, triangle ABC and triangle DEF, sides AB = DE, BC = EF and CA = FD then,

- triangle ABC is congruent to triangle DEF
- triangle ABC is congruent to triangle EFD
- None of the above
- triangle ABC is congruent to triangle FDE

**Q.**

In which of the following situations, an angle bisector construction cannot be used to bisect the angle created between two given lines?

2 intersecting lines

Neither Option 1 nor 2

2 parallel lines

Both Options 1 & 2

**Q.**

Prove that in a parallelogram with all four sides equal, the diagonals are perpendicular bisector of each other.

**Q.**In the following figure, ABCDis a parallelogram and line segments AE and FC bisect the angles A and C respectively. Show that AE is parallel to FC

**Q.**Two triangles are said to be congruent if the sides and angles of one triangle are ___ the corresponding sides and angles of the other triangle.

- lesser than
- not equal to
- greater than
- equal to

**Q.**In triangles ABC and XYZ, AB = XY, BC = YZ and ∠B = ∠Y, 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.**

In the given parallelogram ABCD, DP = BQ and ∠ADP=∠CBQ. To which triangle is ΔADP congruent to?

ΔCBQ

ΔPDQ

ΔQBC

ΔPQB

**Q.**

In a triangle ABC, AB = AC. Suppose P is point on AB and Q is a point on AC such that AP = AQ. Prove that ΔAPC ≅ ΔAQB.

**Q.**

Let ABCD be a parallelogram and suppose the bisectors of ∠A and ∠B meet at P. Prove that ∠APB = 90°.

**Q.**By applying SAS congruence condition, state which of the following pairs of triangles are congruent. State the result in symbolic form

**Q.**

Two triangles have five pairs of congruent parts, but still, the triangles are not congruent.

False

True

**Q.**Sides opposite to the equal angles of a triangle are not equal.

- True
- False

**Q.**

In the figure, ABCD is a parallelogram and AP = CQ. Prove that PD = BQ. Prove also that the quadrilateral PBQD is a parallelogram.

**Q.**

In a triangle ABC, AC = AB and the altitude AD bisects BC. Prove that ΔADC ≅ ΔADB.

**Q.**

Let ABCD be a rectangle and let P, Q, R, S be the mid-points of AB, BC, CD, DA respectively. Prove that PQRS is a rhombus.

**Q.**

Suppose ABC is a triangle and D is the midpoint of BC. Assume that the perpendiculars from D to AB and AC are of equal length. Prove that ABC is isosceles.

**Q.**ABCD is a rhombus in which the altitude from D to side AB bisects AB. Find the angles of the rhombus. [4 MARKS]

**Q.**

In ΔPQR, PQ = QR; L, M and N are the midpoints of the sides of PQ, QR and RP respectively. Prove that LN = MN.

**Q.**

(v) All the angles of a _ figure are equal.

**Q.**In figure AB=AD and ∠BAC=∠DAC.

(i) Identify the congruent triangles.

(ii) Find congruent parts for each of the following

(a) ∠ABC

(b)∠ACD