Draw two parallel lines using a ruler and verify whether they are parallel to each other by construction

HARD

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment of length

7.8 cm

and divide it in the ratio

5 : 8

. Write the measurement of both parts.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment of length

7.6 cm

and divide it in the ratio

5 : 8

.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a triangle

A B C

with side

B C = 7 cm

.

∠ B = 45 °

and

∠ A = 105 °

. Then, construct another triangle whose sides are

\frac{4}{3}

times the corresponding sides of triangle

A B C

.

HARD

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw

\bar{A B}

of length

7.4 cm

and divide it in the ratio

5 : 7

. Write the construction steps.

HARD

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

A B = 7 cm

. Draw

A C

making an angle of

60 °

with

A B

. Mark

A C = 4 c m

. Through

C

, draw a line parallel to

A B

.

HARD

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Mark three non-collinear points

A, B, C

and draw

∆ A B C

. Through each vertex of the triangle, draw a line parallel to the opposite side

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

X Y = 9 cm

.Take a point

A

above

X Y

. Construct a line parallel to

X Y

passing through point

A .

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

E F

. Mark a point

G

outside it. Draw

H J

to pass through

G

and parallel to

E F

.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Habib has drawn a line segment

P Q

on his exercise book and he has also considered a point

R

outside the line segment

P Q

. A line, parallel to the line segment

P Q

is drawn that passes through

R

. The final diagram will look like,

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line, say

A B,

take a point

C

outside it. Through

C,

draw a line parallel to

A B

using ruler and compasses only.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line

' l'

. Construct a line

m

parallel to

l

at a distance of

5 cm

.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

X Y = 5 cm

. Take a point

A

above

X Y

. Construct a line parallel to

X Y

passing through point

A

.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line $A B$ . Take a point $P$ outside it. Draw a line passing through $P$ and parallel to $A B$ .

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

P Q = 5 cm

. Take a point

B a b o v e P Q

. Construct a line parallel to

P Q

passing through point

B

. Find the distance between the parallel lines.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

During construction of a line parallel to a given line from a point P outside this line (shown in the figure), the radius of drawn arc around the point P is _____ of that around the point Q.

Question Image

EASY

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Write the quadrants in which the following points lie:

$(- 4, 7)$

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Let

l

be a line and

P

be a point not on

l

. Through

P,

draw a line

m

parallel to

l

. Now join

P

to any point

Q

on l. Choose any other point

R

on

m

. Through

R,

draw a line parallel to

P Q .

Let this meet

l

at

S .

What shape do the two sets of parallel lines enclose?

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw two parallel lines at a distance

5 cm

apart.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line

P Q

. Draw another line parallel to

P Q

at a distance of

3 cm

from it.

MEDIUM

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Draw a line segment

P Q = 7 cm

. Mark a point

O

above it. Through

O

draw a line parallel to

P Q

.

Draw two parallel lines using a ruler, and verify whether they are parallel to each other by construction.

Important Questions on Congruence

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