Given Base, Base Angle and Sum of Other Two Sides

Q. The construction of a triangle PQR, given that PQ = 5 cm, $\angle Q={45}^{\circ }$ is not possible when sum of PR and QR is equal to

1. 
   8 cm
2. 
   9 cm
3. 
   7 cm
4. 
   4 cm

Q.

Construct a $\Delta ABC$ in which $AB=5.8cm,\angle B={60}^{\circ }$ and $BC+CA=8.4cm$. Justify your constructions.

Q.

$Constructa\Delta ABCinwhichBC=4.5cm,\angle B={45}^{\circ }andAB+AC=8cm\text{Justify your constructions.}$

Q.

Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.

Q.

Using paper folding to construct a line perpendicular to a given line through a point fold the paper through the point so that the given line segment lies:

1. Perpendicular to the papers edge

2. On the point

3. At an angle

4. Upon Itself

Q.

Using ruler and compasses only, construt a $△ABC,$ given base BC = 7 cm, $△ABC={60}^{\circ }$ and AB + AC = 12 cm.

Q.

Construct right triangle whose one side is 3.5cm and the sum of the other side and the hypotenuse is 5.5cm.

Q.

Construct an equilateral triangle of side $6cm$ and mark the incircle.

Q. Construct an isosceles triangle whose two equal sides measure 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex

Q. Construct a right triangle whose base is 6cm and the sum of its hypotenuse and other side is 18 cm.

Q. Question 5
Construct a $\Delta ABC$ in which BC =5cm, $\angle B={60}^{\circ }$ and AC + AB = 7.5cm.

Q.

Construct a $△ABC$ in which $BC=3.6cm,AB+AC=4.8cm$ and $\angle B={60}^{\circ }$.

Q.

Construct a $△$ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and $\angle B={45}^{\circ }$.

Q. Question 5
Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm

Q.

The construction of a $∆ABC$ in which $AB=6cm$, $\angle A=45°$ is possible when $(BC+AC)$ is

1. $7cm$

2. $5cm$

3. $5.8cm$

4. $4.9cm$

Q.

Which of the following figures show the correct method to construct a triangle if we know its base, a base angle and sum of other two sides?

1. 

2. 
3. 
4. 

Q.

For constructing a triangle with a given base, a base angle and difference between the other two sides, a ___ bisector is required.

Q.

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the trees is:

1. 11 m

2. 31 m

3. 15 m

4. 9 m

Q.

Construct the right-angled $\text{△PQR}$, where $\text{m∠Q = 90°}$, $\text{QR = 8 cm}$ and $\text{PR = 10 cm}$.

Q. Construct a triangle $ABC$ in which $BC=7cm$, $\angle B={75}^o$ and $AB+AD=13cm$.

Q.

The construction of $\Delta$ABC, given that BC = 12 cm, is possible when the difference of AB and AC equals

1. 12.5 cm

2. 8 cm

3. 10 cm
4. 14 cm

Q.

A triangle ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and DB = 45${}^{\circ }$ can be constructed using compass and ruler.

1. True
2. False

Q. Construct a triangle XYZ in which $\angle Y$ = ${30}^0$ , $\angle Z$ = ${90}^0$ and XY + YZ + ZX = 11 cm .

Q. It is impossible to construct $\Delta \text{ABC}$ with BC= 5.5 cm and $\angle C={60}^{\circ }$ with AB+AC=

1. 5.9 cm
2. 6 cm
3. 4.5 cm
4. 5.7 cm

Q.

Q.

During the construction of a triangle given its base, a base angle and the sum of other two sides, which of the triangles formed are congruent?

1. $△$ ABC and $△$ AMC
2. $△$ ABC and $△$ ADC
3. $△$ ABC and $△$ AMD
4. $△$ AMC and $△$ AMD

Q.

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows:

1. Draw a line segment, say XY equal to AB + BC + AC

2. Make angles LXY equal to $\angle$ B and MYX equal to $\angle$ C

3. Bisect $\angle$ LXY and $\angle$ MXY. Let these bisectors intersect each other at A.

4. Draw perpendicular bisectors PQ of AX and RS of AY

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

6. The triangle ABC is thus formed.

How many isosceles triangles are there in this figure?

1. 0

2. 1

3. 2

4. 4

Q. Construct $△LMN$ in which base $MN=7cm$, $\angle LMN={75}^{\circ }$ and $LM+LN=9cm.$

Q.

Write true or false for the given statement:

A triangle$ABC$ can be constructed in which $AB=5cm,\angle A=45°andBC+AC=5cm$.

1. True
2. False

Q. Construct a triangle in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 4 cm. Draw a circle circumscribing the triangle ABC. The radius of the circle is:

1. 2.82 cm
2. 3 cm
3. 4.5 cm
4. 5.65 cm