Proof for Validity of Construction of a Perpendicular Bisector

Q. Prove that every line segment has a unique midpoint.

Q.

Any point on the perpendicular bisector of a line segment is equidistant from the end points of the segment.

1. True
2. False

Q. $ABCD$ is a quadrilateral in which $AD=BC$ and $\angle DAB=\angle CBA$ . Prove that
(i) $△ABD\cong △BAC$
(ii) $BD=AC$
(iii) $\angle ABD=\angle BAC$

Q. Using ruler and compasses only, draw an angle of measure 135°.

Q.

A ___ bisector divides the line segment into two equal halves and the angles thus formed are both right angles.

Q.

In $\Delta$ ABD, AB=AD and AC is perpendicular to BD. State the property by which $\Delta$ ACB $\cong$ $\Delta$ ACD.

1. SAS property

2. SSS property

3. RHS property

4. ASA property

Q. Line $l$ is the bisector of an angle $\angle A$ and $B$ is any point on $l$. $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $\angle A$. Show that:
(i) $△ABP\cong △AQB$
(ii) $BP=BQ$ or $B$ is equidistant from the arms of $\angle A$.

Q.

In the below figure if AP=BP, AQ=BQ, then AM=BM?

1. True
2. Data insufficient
3. False
4. Cannot be determined

Q. Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.

Q.

In the below figure if AP=BP, AQ=BQ, then AM=BM?

1. True
2. False
3. Data insufficient
4. Cannot be determined

Q.

Each point on a/an _________ is such that it forms an isosceles triangle with the end points of the given line segment.

1. perpendicular bisector
2. angular bisector
3. altitude
4. median

Q. A ___ bisector divides the line segment into two equal halves and the angles thus formed are both right angles.

1. perpendicular
2. non-perpendicular
3. parallel
4. non-parallel

Q. P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

Q.

Each point on a/an _________ is such that it forms an isosceles triangle with the end points of the given line segment.

1. perpendicular bisector
2. angular bisector
3. altitude
4. median

Q. congruency rule is used to prove the construction of a perpendicular bisector.

1. SSS
2. RHS
3. ASS

Q. Which congruency rule(s) is/are used to prove the construction of a perpendicular bisector?

1. SAS
2. SSS
3. RHS
4. ASS

Q.

A ___ bisector divides the line segment into two equal halves and the angles thus formed are both right angles.

Q. In the adjoining figure, PQ$=$PR and QL$=$MR. Prove that PL$=$PM.

Q. Using your protractor, draw an angle of measure 108°. With this angle as given, draw an angle of 54°.

Q. If the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles.
If true then enter 1 else if False enter 0

Q.

Each point on a/an _________ is such that it forms an isosceles triangle with the end points of the given line segment.

1. perpendicular bisector
2. angular bisector
3. altitude
4. median

Q.

In quadrilateral $ACBD,AC=AD$ and $AB$ bisects $\angle A$. Show that $△ABC\cong △ABD$. What can you say about $BC$ and $BD$?

Q.

In the below figure if AP=BP, AQ=BQ, then AM=BM?

1. True
2. False
3. Data insufficient
4. Cannot be determined

Q. How many triangles are there in the diagram given below?

1. 6
2. 10
3. 12
4. 14