SAS Postulate

Q. In figure, line segment DF intersects the side AC of a $\Delta ABC$ at the point E such that E is the mid – point of CA and $\angle AEF$ and $\angle AFE$. Prove that $\frac{BD}{CD}=\frac{BF}{CE}$

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.

1. SSA
2. SSS
3. RHS
4. 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 $\angle DAB=\angle CBA$(See the given figure). Prove that
$\Delta ABD\cong \Delta BAC$

Q.

A triangle can be drawn if two sides and $\_\_\_\_\_$ angle are given.

1. included

2. any

3. no

4. not sure

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

1. triangle ABC is congruent to triangle DEF
2. triangle ABC is congruent to triangle EFD
3. None of the above
4. 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?

1. 2 intersecting lines

2. Neither Option 1 nor 2

3. 2 parallel lines

4. 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.

1. lesser than
2. not equal to
3. greater than
4. 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?

1. A.S.A. criterion
2. S.A.S. criterion
3. A.A.A. criterion
4. S.S.S. criterion

Q.

In the given parallelogram ABCD, DP = BQ and $\angle ADP=\angle CBQ$. To which triangle is $\Delta ADP$ congruent to?

1. $\Delta CBQ$

2. $\Delta PDQ$

3. $\Delta QBC$

4. $\Delta PQB$

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.

1. False

2. True

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

1. True
2. 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. $\text{In figure}AB=AD\text{and}\angle BAC=\angle DAC.$
(i) Identify the congruent triangles.
(ii) Find congruent parts for each of the following
$\text{(a)}\angle ABC$
$\text{(b)}\angle ACD$