Geometry

Geometry

by Manju Sengar

Multiple Choice

The idea of equal alternate angles is used to construct which of the following?

• A line parallel to a given line

• A triangle

• A Square

• Two Trinagles

Multiple Choice

A line p and a point X not on it are given. Which of the following is used to draw a line parallel to p through X?

• Equal corresponding angles.

• Congruent triangles

• Angle sum property of triangles

• Pythagoras’ theorem.

Multiple Choice

Δ PQR is such that ∠P = ∠Q = ∠R = 60° which of the following is true?

• Δ PQR is equilateral.

• Δ PQR is acute angled

• Both [a] and [b]

• Neither [a] nor [b]

Multiple Choice

How many perpendicular lines can be drawn to a line from a point not on it?(a) 1(b) 2(c) 0(d) Infinite

• 1

• 0

• 2

• infinite

Multiple Choice

In which of the following cases can a triangle be constructed?

• Measures of three sides are given.

• Measures of two sides and an included angle are given

• Measures of two angles and the side between them are given.

• All the above

​Draw an ∠BAC of measure 50 degree such that AB = 5 cm and AC = 7 cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersecting each other at D. Measure BD and CD

​CONSTRUCTING A TRIANGLE WHEN THE LENGTHS OF ITS THREE SIDES ARE KNOWN (SSS CRITERION) 

 

​Construct a triangle ABC, given that AB = 5 cm, BC = 6 cm and AC = 7 cm.

Step 1 First, we draw a rough sketch with given measure.

 

 

Step 2 Draw a line segment BC of length 6 cm.

 

Step 3 From B, point A is at a distance of 5 cm. So, with B as centre, draw an arc of radius 5 cm 

 

​Step 4 From C, point A is at a distance of 7 cm. So, with C as centre, draw an arc of radius 7 cm

 

Step 5 A has to be on both the arcs drawn. So, it is the point of intersection of arcs. Mark the point of intersection of arcs as A. Join

​Construct ∆XYZ in which XY= 4.5 cm, YZ = 5 cm and ZX = 6 cm.

​CONSTRUCTING A TRIANGLE WHEN THE LENGTHS OF TWO SIDES AND THE MEASURE OF THE ANGLE BETWEEN THEM ARE KNOWN. (SAS CRITERION)

Construct a triangle PQR, given that PQ = 3 cm, QR = 5.5 cm and ∠PQR = 60°.

 

 

Step 1 First, we draw a rough sketch with given measures.