Perpendicular Bisector

Q.

For which of the following can a perpendicular bisector be drawn?

1. Line

2. Ray

3. Line segment

4. None of These

Q.

For constructing a right angle without a protractor, which of the following method/s is/are used?

1. Angle Bisector

2. ${60}^{\circ }$ angle construction

3. Median

4. Construction of triangle

Q.

In the figure ABCD is a square, M, N, O and P are the midpoints of sides AB, BC, CD and DA respectively. Identify the congruent triangles.

Q.

What is the minimum arc radius that can be drawn during the construction of a perpendicular bisector, given that line segment has length L?

1. L

2. L/4

3. L/2

4. L/3

Q.

In the given construction,

• PQ is the perpendicular bisector AX
• RS is the perpendicular bisector AY
• XA is the angle bisector of the $\angle LXY$
• YA is the angle bisector of the $\angle MYX$

Then $\angle CAB$ will be

Q.

Divide 714 Marbles between Alok and Kabir in the ratio 3 : 4

Q. A line segment of a specific length is provided to you. Is it possible to replicate the same line segment without using a ruler?

1. Yes, it is possible to replicate a line segment of specific length without a ruler.
2. No, it is not possible to replicate a line segment of specific length without a ruler.

Q.

Suppose ABCD is rectangle. Using RHS theorem, prove that triangles ABC and ADC are congruent.

Q.

Let ABCD be a square and let points P on AB and Q on DC be such that DP = AQ. Prove that BP = CQ.

Q.

In the given figure AD = BC and BD = CA. Choose the correct criterion for △ABD ≅ △BAC.

1. ASA

2. SSS

3. SAS

4. RHS

Q.

Two triangles ABC and DBC have common base BC. Suppose AB = DC and ∠ABC = ∠BCD. Prove that AC = BD.

Q.

Let AB, CD be two line segments such that AB || CD and AD || BC. Let E be the midpoint of BC and let DE extended meet AB in F. Prove that AB = BF.

Q.

With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet in X and Y as shown. Join XY

These are the two statements:
Statement 1: AB is the perpendicular bisector of XY
Statement 2: XY is the perpendicular bisector of AB
Choose the correct option from below.

1. Only Statement 1 is true

2. None of the statements is true

3. Only Statement 2 is true

4. Both the statements are true

Q. If AB is made equal to BC in the given figure, then AD : DC = _____.

1. 1:2
2. 2:1
3. 3:2
4. 1:1

Q. Which of the following is incorrect for the following figure?

1. AB = BC
2. AB $\ne$ AD
3. AD = BC
4. AB = DC

Q.

Pair of congruent triangles and incomplete statements related to them are given below. Observe the figures carefully and fill up the blanks:

(a) In the adjoining figure if ∠C = ∠F, then AB = ---------- and BC = ----------.

(b) In the adjoining figure if BC = EF, then ∠C = --------- and ∠A = ----------.

(c) In the adjoining figure, if AC = CE and ΔABC ≅ ΔDEC, then ∠D = -------- and ∠A = ---------.

Q.

In a trapezium ABCD with AB || CD, it is given that AD is not parallel to BC. Is ΔABC ≅ ΔADC? Give reasons.

Q. In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE || BC.

Q. A line segment $\overline{AB}=4.6cm$ Another $\overline{CD}=3.8cm$. Then measure of the line segments whose length is equal to the difference of $\overline{AB}and\overline{CD}$

1. $1.8cm$
2. $2.8cm$
3. $0.8cm$
4. $8.4cm$

Q. The bisector of an angle lies in its

1. On the arms of the angle
2. Exterior
3. Interior
4. Any where in the plane

Q.

Based on the construction below, which of the given options must be true?

​​

1. m ABD = m CBD

2. m ABD = m CBD

3. m ABD = m ABC

4. m CBD = m ABD

Q. Match the figures with its proper names.

1. Bisector
2. ∠ bisector
3. ⊥ bisector

Q.

In the given construction,

• PQ is the perpendicular bisector AX
• RS is the perpendicular bisector AY
• XA is the angle bisector of the $\angle LXY$
• YA is the angle bisector of the $\angle MYX$

Then find the value of $\angle CAB$.

Q. Draw a circle and mark an arc LMN on this circle. Then, inscribe an angle LMN in it.

How many more angles can you inscribe in this arc?

Q. On bisecting 50°, the two angles of each half are:

1. 20°, 30°
2. 15° , 35°
3. 25°, 25°
4. 40°, 10°

Q. Construct a rectangle having adjacent sides of $6cm$ and $4cm$ and find its area

Q.

In the adjoining figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that DE || BC. [Hint:- use the concept of alternate angles.]