Construct Triangle When Its Base, Sum of the Other Two Sides and One Base Angle Are Given

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

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

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

Q.

Construct a triangle $ABC$ with the following data:

$AB=5\mathrm{cm},\mathrm{BC}=6\mathrm{cm}\mathrm{and}\angle \mathrm{ABC}=90°$

(i) Find a point$P$ which is equidistant from $B\mathrm{and}C$ and which is$5\mathrm{cm}$ from$A.$ How many such points are there?

(ii) Construct an inscribed circle of $∆ABC$ drawn above.

Q. Steps for the construction of a triangle ABC in which AB=5.8cm, BC+CA=8.4cm and $\angle B={60}^{\circ }$ is given below.Choose the correct order.

1.Join AC
2.From the segment BX, cutoff line segment BD of length 8.4cm.Join AD
3.Draw the perpendicular bisector of AD and let it meet BD at C.
4.Draw a line segment AB of length 5.8cm
5..Draw a line segment BX , sufficiently large such that $\angle ABX={60}^{\circ }$

1. 4, 5, 2, 1, 3
2. 4, 2, 5, 1, 3
3. 4, 1, 5, 2, 3
4. 4, 5, 2, 3, 1

Q.

Construct each of the following and give justification: A triangle $PQR$ given that $QR=3\mathrm{cm},\angle PQR={45}^{°},\mathrm{and}QP-PR=2\mathrm{cm}$.

Q.

Construct kite EASY with EA = 2cm, AS = 5cm, ES = 6cm.

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. It is not possible to construct $\Delta \text{ABC}$ given that BC = 5.5 cm and $\angle C={60}^{\circ }$, when sum of the measures of AB and AC equal to ___.

1. 5.9 cm
2. 6 cm
3. 4.5 cm
4. 5.7 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. It is not possible to construct $\Delta \text{ABC}$ given that BC = 5.5 cm and $\angle C={60}^{\circ }$, when sum of the measures of AB and AC equal to ___.

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

Q.

A student was given the following details while constructing a triangle ABC:

The length of the base of the triangle BC, one of the base angles say $\angle$ B and the sum of the other two sides of the triangle (AB+AC)

He went about the construction of this triangle by first drawing the base of the triangle BC. He then drew an angle at the point B equal to the given angle on a ray that he drew. After completing these steps, he got stuck and doesn’t know what to do next. Which of the following steps will he take up next?

1. Cut a line segment BD equal to (AB+AC) on that same ray

2. Change the base length to (AB+AC) and then draw one of the base angles at one of the ends of the line segment whose length is equal to (AB+AC)

3. He knows the perimeter of the triangle, he changes the base length to that of the perimeter of the triangle and then draws one of the base angles at one of the ends of the line segment

4. Cut a line segment BD equal to $2(AB+AC)$ on that same ray

Q. arcs are required to draw the perpendicular bisector in triangle construction 1.

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

Q.

Your challenge is to mark the points between the rays PA and PB (both included) which lie at a certain distance, say 'd', from a point P, as shown. PC = d. How many such points exist?

1. 0

2. Only 1 point, on the ray PA

3. Only 2 points, each on the rays PA and PB

4. Infinite points, between the rays PA and PB

Q.

Pinku was a hard working student who used to learn without understanding. He was asked to construct a triangle say ABC and was given the base length of the triangle BC, one of the base angles say $\angle$ B and the sum of the other two sides (AB + AC). He went about constructing the triangle in the following way:

He drew the base BC with the given dimension, drew the $\angle$ B along the ray BX with the angle known to him already. He then took B as centre and (AB + AC) as radius and cuts an arc on the ray BX intersecting the ray at D.

He then joins D to C. He then draws a perpendicular bisector of the line DC and the perpendicular bisector intersecting on the ray intersects the ray at point A. The teacher then asked him as to why he did what he did, she started from the back and asked him as to how the intersection of the ray and the perpendicular bisector gives A.

Which of the following is the reason for him drawing the perpendicular bisector and intersecting it with the ray?

1. Since the perpendicular bisector would get AD = AC which is like flipping the point D about the perpendicular bisector and merging it with point C

2. To get point A is the mid point of the line segment BD

3. To get $△$ ABC and $△$ ADC congruent

4. To get $△$ ABC and $△$ ADC congruent

Q. Steps for the construction of a triangle ABC in which AB=5.8cm, BC+CA=8.4cm and $\angle B={60}^{\circ }$ is given below.Choose the correct order.

1.Join AC
2.From the segment BX, cutoff line segment BD of length 8.4cm.Join AD
3.Draw the perpendicular bisector of AD and let it meet BD at C.
4.Draw a line segment AB of length 5.8cm
5..Draw a line segment BX , sufficiently large such that $\angle ABX={60}^{\circ }$

1. 4, 5, 2, 1, 3
2. 4, 2, 5, 1, 3
3. 4, 5, 2, 3, 1
4. 4, 1, 5, 2, 3