Construction of a Triangle with Given Perimeter and Two Base Angles

Q.

Complete the steps to construct a triangle XYZ in which $\angle Y={45}^{\circ },\angle Z={90}^{\circ }$ and XY + YZ + ZX = 13 cm.

Steps of construction:
Step 1: Draw a line segment AB=13 cm
Step 2: At A, Construct an angle of ${45}^{\circ }$ and at B construct an angle of ${90}^{\circ }$
Step 3 will be

1. Bisect these angles. Let bisector of these angles intersect at point X.
2. Draw perpendicular bisection CD of AX to intersect AB at Y
3. Join XY and XZ to obtain required
4. Draw perpendicular bisection EF of XB to intersect AB at Z

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

Q.

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

1. True

2. False

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. False

2. True

Q.

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

1. ${55}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

Q.

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

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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. Draw an angle of measure ${135}^o$ and bisect it.

Q. The construction of a triangle is not possible when

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