Construction of a Triangle with SAS Criterion

Q.

Question 3
Construct $\Delta ABC$ with BC = 7.5 cm and $\angle C={60}^{\circ }$, and AC = 5cm.

Q.

Question 2
Construct $\Delta$ PQR if PQ=5cm, $\angle PQR={105}^{\circ }and\angle QRP={40}^{\circ }$.

Q.

Statement $1$: It is possible to construct a triangle when measurements of two sides and one angle are given.

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

Choose the correct option.

1. Statement 1 is right and Statement 2 is wrong

2. Statement 2 is right and Statement 1 is wrong

3. Both the statements are false

4. Both the statements are correct

Q.

Akash was given lengths of two sides and the measure of an angle which is not included between the two sides. But still he was able to draw the triangle. So what should be the angle that was given? (in degrees)

__

Q.

Things required for accurate construction a triangle are

1. Pencil, Ruler, compass, protractor

2. Pencil, Ruler, compass

3. Only pencil

4. Pencil, Ruler

Q. Which angle of $△$POQ corresponds to $\angle$OSR of $△$ROS ?

1. $\angle$POQ
2. $\angle$OQP
3. $\angle$QPO
4. None of the above

Q.

Draw a triangle $ABC$ with side $BC=6cm$, $AB=5cm$ and $\angle ABC={60}^{\circ }$, Then construct a triangle whose sides are$\frac{3}{4}$ of the corresponding sides of the triangle $ABC$.

Q.

The minimum number of triangles that can be drawn if two sides and one angle has been given is __.

Q. Write down the procedure of constructing of a $△ABC$ with $BC=7.5cm,AC=5cm$ and $\angle C={60}^o$

Q.

Which of the following criterion cannot be taken as a prerequisite for the construction of triangles?

1. ASA

2. AAA

3. SSS

4. SAS

Q.

You are given the measurement of the two legs of a right angled triangle. What else do you need in order to draw a triangle?

1. Length of the third side

2. Measure of one angle

3. Either length of one side or measure of one angle

4. Do not need anything else as the triangle can be constructed with the help of the given data

Q. Construct a circumcircle of a right angled triangle with sides $8cm,6cm$ and $10cm$.

Q.

A student of class VII attempts to make a triangle of dimension 2 cm, 3 cm and 6 cm. He drew the longest side first, thereby generating two vertices of the triangle. He could not get the third vertex. What could be the reason?

1. No angle of the triangle is given

2. The sum of two sides is less than the third side

3. The first step is wrong

4. He does not know to draw the arc

Q. Construct $△DEF$ such that $DE=5cm,DF=3cm$ and $m\angle EDF={90}^o$.

Q. Construct a triangle $ABC$, in which $AB=5.5cm,AC=6.5cm$ and $\angle BAC={75}^{\circ }$.
Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) At $A$, construct a line segment $AE$, sufficiently large, such that $\angle BAE={75}^{\circ }$, use protractor to measure ${75}^{\circ }$.
2) Draw a line segment which is sufficiently long using ruler.
3) With $A$ as centre and radius $6.5cm$, draw an arc cutting $AE$ at C. Join $BC$. Hence, $ABC$ is the required triangle.
4) Locate points $A$ and $B$ on it such that $AB=5.5cm$.

1. $2,1,4,3$
2. $2,4,1,3$
3. $4,2,1,3$
4. $1,2,4,3$

Q. Construct a triangle of sides $4cm,5cm$ and $6cm$ and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle. Give the justification of the construction.

Q. Is it possible to construct a triangle $ABC$ in which $BC=8cm,\angle B={40}^{\circ }$ and $AB=AC=3.5cm?$

Q. Construct a triangle $LMN$ in which $LM=7.8cm,MN=6.3cm$ and $\angle LMN={45}^{\circ }$.

Q. Construct $\Delta ABC$ in which $BC=8cm$, $\angle B={45}^o$ and $AB-AC=3.5$ cm.

Q. What is the side included between the angles M and N of $△MNP$?

Q. Construct a triangle $ABC$, given the following
$AB=5.4$ cm, $AC=5$ cm and $\angle A={45}^o$.

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

Q.

Pallav got following question in his exam:

Given the base angles, say $\angle$ B and $\angle$ C and BC + CA + AB, construct triangle ABC.

He followed the following steps for the construction.

1. Draw a line segment, say XY equal to BC + CA + AB.

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

3. Bisect $\angle$ LXY and $\angle$ MYX. Let these bisectors intersect at a point A

4. Draw perpendicular bisectors PQ of AX and RS of AY.

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

1. False

2. True

Q. A student was asked to measure three angles of a triangle, and he finds only one acute angle in the triangle. Did he measure correctly?

1. Yes
2. No, the triangle should have at least two acute angles.
3. No, the triangle should have at least three acute angles.
4. None of the above

Q.

In an isosceles $\Delta ABC$, $\angle A$ is ${30}^{\circ }$. The sides AB and AC are equal. Using constructions, find which side of $\Delta ABC$ is the shortest.

1. BC

2. AC

3. Data Insufficient

4. AB

Q. Draw a triangle $ABC$ with $BC=6cm,AB=5cm$ and $\angle ABC={60}^o$ then construct a triangle whose sides are $4/5$ of the sides of the $△ABC$. Justify.

Q. Construct a $△ABC$ in which $BC=7$ cm, $\angle B={75}^0$ and $AB+BC=13$ cm.

Q.

Which of the following methods or concepts is not used in either method for Triangle construction 1?

1. (a) and (b) above.
2. None of the above

3. Perpendicular Bisector

4. Isoceles Triangle

Q. Construct a $△PQR$ in which $PQ=6.2$ cm, $\angle Q={60}^o$ and $RQ-PR=3$ cm.

Q.

Is it possible to construct an equilateral triangle without using protractor? Why is the method of ${60}^{\circ }$ angle construction the best method for this?
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