Construction of Triangles

Q. State whether the statement is true or false.
A scalene triangle is a type of triangle in which all the three sides have different lengths.

1. True
2. False

Q.

Which of the following could represent the sides of a triangle?

1. 3, 4, 5

2. 1, 2, 3

3. 2, 4, 6

4. All of these

Q.

Construct a triangle XYZ, in which XY = 6 cm, YZ = 8 cm and ZX = 5.5 cm.

Q. If two sides of a triangle are given as 10 cm and 8 cm, then which of the following can be the length of the third side to construct that triangle?

1. 2 cm
2. 19 cm
3. 3 cm
4. Any length less than 2 cm

Q.

A ladder rests against a tree. If it reaches a height of 40 m from the ground, and if the distance between the foot of the ladder and the tree is 30 m, then the length of the ladder is ___ m.

1. 25

2. 45

3. 50

4. 100

Q.

Written:

Construct a triangle PQR, in which PQ = QR = RP = 6 cm.

Q. The exterior angle of a triangle is equal to the sum of angles.

1. interior opposite
2. exterior alternate
3. corresponding

Q.

Construct an equilateral $△XYZ$. Whose sides are $4.5cm$.

Q. In ΔRST, RS = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?

1. ASA criterion
2. SAS criterion
3. SSS criterion
4. RHS criterion

Q. An exterior angle of a triangle measures 110° and it's it's interior opposite angles are in ratio 2:3 find the measurements of these angles

Q. Question 5
Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.
$\begin{array}{ccccc}& Triangle& & Givenmeasurements& \\ 5.& \Delta ABC& BC=2cm& AB=4cm& AC=2cm\end{array}$

Q. Sum of all interior angles of a triangle is ______ degree.

1. 150
2. 90
3. 180
4. 120

Q. A triangle of sides AB = 6 cm, BC = 3 cm and AC = 4 cm is constructed. What is the measure of angle A?

1. 36

Q.

Construct a triangle PQR in which PQ = 6.4 cm, PR = QR = 5 cm

Q.

Written:

Construct a triangle ABC in which BC = 5 cm, AB = AC = 4.5 cm. Name the type of the triangle.

Q.

We can construct a triangle when its two sides and the __________ between them is given.

Q.

In ΔXYZ, if ∠X = ∠Y = 60°, then what is the measure of ∠Z?

Q. Which instrument is preferred to draw an angle of 65 degree easily?

1. Set squares
2. Ruler
3. Compass
4. Protractor

Q. Construct triangles of the measures given below.

Q. If the interior opposite angles of a triangle a are ${52}^{\circ }$ and ${35}^{\circ }$, the corresponding exterior angle will be =

1. ${87}^{\circ }$
2. ${17}^{\circ }$
3. ${78}^{\circ }$

Q. In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:
(i) 5, 7, 9
(ii) 2, 10, 15
(iii) 3, 4, 5

Q. Steps to inscribe an equilateral triangle in a circle of radius 6 ft (Scale : 1 in = 2 ft) are :

Step 1 : Draw a circle with centre 'O' using radius 3 inch.

Step 2 : Mark point A on the circumference and join AO.

Step 3 : ?

Step 4 : Repeat the process with D as centre to obtain point B and continue the same in the anticlockwise direction to further obtain points E and C.

Step 4 : Join AB, BC and CA.

Identify the missing step.

1. With A as the center and a radius equal to AO, mark an arc on the circle using a compass and name the point as D.
2. With A as the center and a radius equal to half of AO, mark an arc on the circle using a compass and name the point as D.
3. With A as the center and a radius equal to twice of AO, mark an arc on the circle using a compass and name the point as D.
4. With A as the center and a radius equal to thrice of AO, mark an arc on the circle using a compass and name the point as D.

Q. The sum of the interior angles of a triangle adds upto degrees.

1. 180
2. 360
3. 90

Q.

Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

Q.

Which of the following tests cannot be undertaken for checking the construction of triangles?

1. ASA Congruency

2. AAA Congruency

3. SSS Congruency

4. SAS congruency

Q.

A ladder $10m$long was rested along a wall such that its top touched the wall at a height of $8m$ from the ground. How far is the foot of the ladder from the wall?

Q.

How many perpendicular bisectors need to be drawn during the method of Triangle Construction 2?

1. 1

2. 2

3. 3

4. 4

Q. The side lengths of a triangle are 10 cm, 5.5 cm, $k$ cm, where $k$ is a whole number. What is the minimum value of $k$?

1. 4
2. 4.5
3. 5
4. 5.5

Q. In a ∆ABC, ∠ABC = 100°, ∠BAC = 35° and BD ⊥ AC meets side AC in D. If BD = 2 cm, find ∠C and length DC.

Q.

Rajeev followed the following steps to construct a triangle $PQR$ such that $PQ=4cm,$ $QR=5cm,$ and $RP=7cm.$

Step 1: Draw a line segment of $QR$ of length $5cm.$

Step 2: Draw an arc of $4cm$ by taking $Q$ as the centre.

Step 3: Mark the intersecting point as $P.$

Step 4: Join $Q,P$, and $Q,R$ to get the required triangle $PQR.$

Which of the following step is missing for constructing this triangle $PQR?$

1. Draw an arc of $7cm$ by taking $R$ as the center.
2. Draw an arc of $7cm$ by taking $Q$ as the center.
3. Draw a line segment of the length of $7cm$ from $R$.
4. Draw a line segment of the length of $7cm$ from $Q$.