Construction 1

Q.

Construct a right triangle whose base is $12\mathrm{cm}$ and sum of its hypotenuse and other side is $18\mathrm{cm}$.

Q. Question 4
Prove that through a given point, we can draw only one perpendicular to a given line.

Q.

Construct a right angle triangle in which hypotenuse $=6.2\mathrm{cm}$ and one side $=4\mathrm{cm}$.

Q.

Pinku was a hard working student who used to mug up without understanding. He was asked to construct a triangle say ABC and was given details like 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 retracked the steps 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 ∆ ABC and ∆ ADC congruent

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

4. None of the above

Q. Construct a triangle ABC in which $BC=7cm,\angle B={75}^{\circ }andAB+AC=13cm$.
[4 Marks]

Q.

Construct each of the following and give justification:

A triangle if its perimeter is $10.4\mathrm{cm}$ and two angles are $45°$ and $120°$.

Q.

Statement 1: It is possible to construct a unique triangle when the measurements of two sides and non-included angle are given.

Statement 2: It is possible to construct a triangle when the measurements of two sides and included angle are given.

Choose the correct option.

1. Both the statements are correct
2. Both the statements are false
3. Statement $1$ is right and Statement $2$ is wrong
4. Statement $2$ is right and Statement $1$ is wrong

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.

The construction of a $∆ABC$ in which $AB=4cm,$ $\angle A=60°$ is not possible when difference of $BC$ and $AC$ is equal to:

1. $3.5cm$

2. $4.5cm$

3. $3cm$

4. $2.5cm$

Q. Arrange the steps to construct a △ABC where BC and sum of sides AB+AC and ∠B is given:

1. Mark D as AB+AC
2. Draw line BC
3. Join point D & C
4. Construct ∠B
5. Bisect a ⊥ to DC

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

4. 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

Q. Construct a △ ABC in which AC = 5 cm, and ∠BAC = 60⁰ and AB – BC = 1.2 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. None of the above

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

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

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

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

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

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

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.