Construction Triangle Whose Perimeter and Base Angles Are Given

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

Q.

Construct right angle triangle PQR in which ∠Q = 90°, QR = 4.5 cm and ∠R = 50°.

Q.

Only an angle bisector is used in the construction of a triangle, given its perimeter and its two base angles.

1. False

2. True

Q. We can draw a triangle if we know its perimeter and one base angle.

1. False
2. True
3. Not always
4. Cannot be predicted

Q.

Which of the following instruments is not used in either method of Triangle Construction 1?

1. Protractor

2. None of these

3. Compass

4. Ruler

Q.

A right triangle with lengths of perpendicular sides 8 cm and 4 cm is constructed. Then the perimeter of this triangle is

1. 21.8 cm

2. 20.9 cm

3. 16.9 cm

4. 15.8 cm

Q. It is easy to construct a triangle if its perimeter and base angles are given.

1. True
2. False

Q.

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

1. 1
2. 3
3. 2
4. 4

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

Q.

A triangle ABC has base angle ${45}^{\circ }$. It's perimeter is $[2+\sqrt{2}]$. What type of triangle is it?

1. Isosceles triangle

2. Right triangle

3. Can't be determined

4. Scalene triangle

Q.

A student constructed a triangle when the perimeter of the triangle and both the base angles are given. The steps of construction he used are as follows:

$\text{1. Draw a line segment, say XY equal to}\text{AB + BC + AC.}$

$\text{2. Make}\angle LXY\text{equal to}\angle B\text{and}\angle MYX\text{equal to}\angle C.$

$\text{3. Bisect}\angle LXY\text{and}\angle MYX.\text{Let these}\text{bisectors intersect each other at A.}$

$\text{4. Draw perpendicular bisectors DE of AX}\text{and FG of AY.}$

$\text{5. Let BQ intersect XY at B and RC}\text{intersect XY at C. Join AB and AC.}$

$\text{6. The triangle ABC is thus formed.}$

$\text{How many isosceles triangles are there}\text{in this figure?}$

1. 0
2. 1
3. 2
4. 4

Q.

Which of the following properties/methods is not used in the construction method of Triangle Construction 3?

1. Only exterior angle of triangle

2. Only perpendicular bisector

3. Only isoceles triangle

4. Exterior angle property and isosceles triangle property

Q.

The exterior angle of a triangle is equal to ___________.

1. sum of all interior angles

2. sum of interior opposite angles

3. the other exterior angle

4. Insufficient data

Q. In the given construction $\angle MYX={60}^{\circ }$, then $\angle AYX$ is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

1. ${55}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${25}^{\circ }$

Q. In the figure given below, which of the pairs of triangles are congruent?(Assume that DE and FG are perpendicular bisectors of AX and AY respectively)

1. $△$ ABX and $△$ ACY
2. $△$ ACR and $△$ YCR
3. $△$ ABC and $△$ ACR
4. $△$ ABQ and $△$ XBQ