Introduction to Geometric Constructions

Q.

To construct an angle of ${60}^{\circ }$ with a compass and ruler,

Steps of construction are:
Step1: Draw a ray AB
Step 2 will be

1. Using protractor, draw an angle ${60}^{\circ }$

2. Taking D as center and any radius, draw an arc intersecting the previous arc at E

3. Taking D as center and same radius, draw an arc intersecting the previous arc at E

4. Taking A as centre and any convenient radius, draw an arc intersecting ray AB at a point D.

Q.

What is the meaning of the word bisect?

1. To divide into 3 parts

2. To cut something into 2 equal halves

3. To cut something into 5 equal pieces.

4. To cut something into 10 pieces.

Q.

Follow the following steps of constructions:

1) Draw a line segment OA.

2) With O as center and a short radius, draw an arc that cuts OA at B.

3) With B as center and the same radius (as in step 2), draw an arc that cuts the first arc at C.

4) With C as center and the same radius (as in step 2), draw an arc that cuts the first arc at D.

5) With C and D as centers, draw two arcs with equal radii such that they intersect at E.

6) Join O and E. What’s the measure of $\angle AOE$ ?

1. ${60}^{\circ }$

2. ${45}^{\circ }$

3. ${75}^{\circ }$

4. ${90}^{\circ }$

Q.

What does a geometry box consist of? What are the main instruments used for construction? [1 MARK]

Q.

What is the relationship between perpendicular lines?

Q.

Why are accurate constructions necessary? [1 MARK]

Q.

Ali was asked to construct a square ABCD for which, the diagonal AC alone is given. He was given a compass and a straight edge (a ruler with NO markings). P is said to be the point of intersection of the diagonals of the square. Which of the following will be Alis second step of construction?

1. Side AB

2. Point P

3. Diagonal AC

4. Perpendicular bisector of AC

Q.

If $△ABC\cong △DEF$and $AB=6cm$ then side $DE$ is:

1. $5cm$

2. $6cm$

3. $7cm$

4. $8cm$

Q. The two edges of a straight road are examples for lines.

1. parallel
2. perpendicular
3. intersecting

Q. It is not possible to construct an angle bisector for a reflex angle.

1. True
2. False

Q. Two lines are said to be __________to each other if they meet at right angles.

1. straight
2. perpendicular
3. transversal
4. parallel

Q. Choose those times at which the minute hand of a clock is perpendicular to the hour hand.

1. 4:00
2. 9:00
3. 6:30
4. 3:30

Q. If any two sides and one angle of △ABC is congruent to any two sides and an angle of △PQR, then the two triangles are congruent.

1. False
2. True

Q. If three angles of a triangle are given, then a unique triangle can be drawn.

1. False
2. True

Q. We can construct $\angle {120}^{\circ }$ with the help of a ruler and compass.

1. False
2. True

Q. Sort the steps to construct an angle of ${60}^0$.

1. $\mathrm{Draw}a\mathrm{line}l\mathrm{and}\mathrm{mention}a\mathrm{point}O\mathrm{on}\mathrm{it}.$
2. $\mathrm{Join}O\mathrm{and}B.\mathrm{Extend}\mathrm{OB}\mathrm{to}\mathrm{get}a\mathrm{ray}.$
3. $\mathrm{With}O\mathrm{as}\mathrm{center}\mathrm{and}a\mathrm{short}\mathrm{radius},\mathrm{draw}\mathrm{an}\mathrm{arc}\mathrm{that}\mathrm{cuts}\mathrm{line}l\mathrm{at}A.$
4. $\mathrm{With}A\mathrm{as}\mathrm{center}\mathrm{and}\mathrm{the}\mathrm{same}\mathrm{radius}\left(\mathrm{as}\mathrm{in}\mathrm{step}2\right),\mathrm{draw}\mathrm{an}\mathrm{arc}\mathrm{that}\mathrm{cuts}\mathrm{the}\mathrm{first}\mathrm{arc}\mathrm{at}B.$