Given Perimeter and Two Base Angles

Q.

Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to ${60}^{\circ }$.

Q.

Using ruler and compasses only, construct a $△$ABC, from the following data :

AB + BC + CA = 12 cm, $\angle B={45}^{\circ }and\angle C={60}^{\circ }$.

Q.

$Constructa\Delta ABCinwhich\angle B={45}^{\circ },\angle C={60}^{\circ },\text{and the perpendicular from the vertex A to base BC is 4.5cm}$

Q.

Construct a triangle whose perimeter is $6.4cm$, and angles at the base are ${60}^{\circ }and{45}^{\circ }$ .

Q. How to draw a triangle whose perimeter and ratio of sides are given.

Q. In the given construction of a $\Delta ABC$, find $\angle CAB$.

Q.

Construct a triangle XYZ in which $\angle Y={30}^{\circ },\angle Z={90}^{\circ }andXY+YZ+ZX=11.$

Q. Observe the construction given below.
To construct triangle ABC, the given components are

1. Its perimeter and two base angles
2. Its base, a base angle and the sum of other two sides
3. Its base, a base angle and the difference of other two sides
4. Its base, a base angle and perimeter

Q.

Construct a square of 9 cm and construct a triangle ADE of area equal to the area of this square ABCD. Which of the following illustrates the construction involved.

1. 

2. 

3. 

4. 

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

[4 marks]
[NCERT]
[Construction of Triangles : Given Perimeter and Two Base Angles]

Q. Construct $△XYZ$ in which $\angle Y={30}^o,\angle Z={60}^o$ and $XY+YZ+ZX=10$ cm.

Q.

$\text{Construct a triangle whose perimeters 10.4 cm and the base angles are}{45}^{\circ }and{120}^{\circ }$

Q. Construct a triangle $ABC$, whose perimeter is $12cm$ and whose sides are in the ratio $3:4:5$

Q.

$\text{Construct a}\Delta ABC\text{whose perimeter is 11.6cm and the base angles are}{45}^{\circ }and{60}^{\circ }$

Q.

Construct any pentagon ABCDE and then construct a triangle (PCQ) of area equal to the area of ABCDE and one of whose vertices in C. Which of the following is the correct diagram for the triangle PCQ?

1. 

2. 

3. 

4. 

Q. Construct a triangle ABC whose perimeter 12 cm and who base angles are ${50}^{\circ }$ and ${80}^{\circ }$.

Q. In the given construction of a $\Delta ABC$, $\angle CAB$ will be

1. ${55}^{\circ }$
2. ${45}^{\circ }$
3. ${65}^{\circ }$

Q. In the given construction of a $\Delta ABC,$ what is the value of $\angle CAB?$

Q.

The steps to construct a triangle with given base angles $\angle$ B and $\angle$ C and BC + CA + AB, are:.
A. Draw a line segment, say XY equal to BC + CA + AB.
B. Make $\angle$ LXY equal to $\angle$ B and MYX equal to $\angle$ C.
C. Bisect $\angle$ LXY and $\angle$ MYX. Let these bisectors intersect at a point A.
D. Draw perpendicular bisectors PQ of AX and RS of AY.
E. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

1. True

2. False

Q. Construct a triangle $ABC$, whose perimeter is $12cm$ and whose sides are in the ratio $2:3:4$.

Q.

What is the correct diagram to construct a parallelogram (EFDC) with one of the angle equal to 'x' and whose area is equal to that of the given triangle (ABC).

1. 

2. 

3. 

4. 

Q.

For the construction of a triangle by the method of Triangle Construction 3, how many pieces of information/data need to be provided?

__

Q. Using the information given in the figure, match the following given AB = CD

1. 24 cm
2. 13 cm
3. 5 cm
4. 12 cm

Q. Construct a triangle $PQR$ in which $\angle Q={60}^o$ and $\angle R={45}^o$ and $PQ+QR+PR=11cm$.

Q. Construct a triangle $ABC$ whose perimeter $12cm$ and whose base angles are ${50}^{\circ }$ and ${80}^{\circ }$

Q.

Construct a triangle whose perimeter is 6.4 cm, and angles at the base are ${60}^{\circ }and{45}^{\circ }$ .

Q. A triangle ABC can be constructed in which$\angle B={60}^o$, $\angle C={45}^o$ and AB +BC + AC = 11 cm. Is this Statement true?

1. True
2. False

Q. To construct a triangle ABC in which $\angle B={60}^{\circ },\angle C={45}^{\circ }$ and AB + BC + AC = 12 cm

The steps of construction are:
Step 1: Draw a line segment XY=12 cm
Step 2: At X, construct an angle of ${60}^{\circ }$ and at y construct an angle of ${45}^{\circ }$
Step 3: Bisect these angles. Let bisector of these angles intersect at point A
Step 4 will be

1. Join AB and AC to obtain required $\Delta ABC$
2. Draw perpendicular bisector PQ of XA to intersect XY at B and RS of YA to intersect XY at C
3. Draw perpendicular bisector PQ of XB to intersect XY at B and RS of YC to intersect XY at C
4. Bisect these angles.Let bisector of these angles intersect at point A

Q. Question 18
If ABC is a right angled triangle such that AB = AC and bisector of angle C intersects the side AB at D, then prove that AC + AD = BC.

Q.

To construct the triangle which one of the following is useful?

1. The area of a triangle.

2. Only one side

3. One side and a base angle

4. The perimeter and the two base angles.