Construction of Right Angle Triangle When One Side and Hypotenuse is Given

Q. Construct a triangle PQR, given that PQ = 5 cm, QR = 8 cm and $\angle PQR={45}^{\circ }$. [4 MARKS]

Q. A right triangle DEF is constructed with DE = 6 cm, $\angle E={90}^{\circ }$ and EF = 8 cm. Choose the correct statement from the following.

1. DF is the hypotenuse of $\Delta$ DEF of length 11 cm
2. DF is the hypotenuse of $\Delta$ DEF of length 12 cm
3. DF is the hypotenuse of $\Delta$ DEF of length 9 cm
4. DF is the hypotenuse of $\Delta$ DEF of length 10 cm

Q. A triangle ABC is constructed with AB = 5 cm, BC = 9 cm and $\angle A={90}^{\circ }$. Then, the length of third side is

1. 6.98 cm
2. 6.42 cm
3. 7.48 cm
4. 8.24 cm

Q. A right angle triangle can be constructed if the measurement of hypotenuse and of the sides is given.

1. one
2. two
3. three
4. four

Q. (a) Construct $\Delta PQR$, given $\overline{PQ}=3.5cm,\overline{PR}=4.5cm$, and $\overline{QR}=5.5cm$

(b) Construct ΔPQR, when PQ = 4 cm, QR = 6 cm and ∠PQR = 60${}^{\circ }$. [4 MARKS]

Q. Question 2
Construct a right triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

Q. A triangle ABC is constructed with AB = 3.5 cm, BC = 6 cm and $\angle A={90}^{\circ }$. Then the length of the third side is

1. 4.87 cm
2. 3.74 cm
3. 3.54 cm
4. 4.64 cm

Q. Construct a right angled triangle ABC with sides AB = 3 cm, BC = 5 cm and $\angle A={90}^{\circ }$

Q. Steps of construction of a right triangle which has hypotenuse of 5 cm and one of the two sides of 3 cm length

1. $MarkintersectionasC$
2. $JoinC,B$
3. $Draw5cmarcfromB$
4. $DrawlineABof3cm$
5. $Mark{90}^{o}atA$

Q. For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. Equilateral triangle
2. Right angled triangle
3. Scalene triangle
4. None of the above

Q. Raman was given the 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)

1. 60${}^{\circ }$
2. 90${}^{\circ }$
3. 30${}^{\circ }$
4. 45${}^{\circ }$

Q. Few measurements of ΔDEF are EF=8.4 cm, ∠E=103⁰ and ∠F=85⁰. Which of the following is correct?

1. ΔDEF can be constructed.
2. ΔDEF is a right angled triangle
3. ΔDEF cannot be constructed.
4. ΔDEF is an acute angled triangle.

Q. A triangle ABC is constructed with AB = 6 cm, BC = 8.48 cm and $\angle A={90}^{\circ }$. Then, the triangle formed is

1. an isosceles right angle triangle
2. a scalene right angle triangle
3. an equilateral triangle
4. an obtuse right angle triangle

Q.

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

(Hint: Recall angle sum property of a triangle).

Q.

Vikas followed the steps given below to construct a triangle

Right-angled triangle LMN, with hypotenuse $LN=8\text{cm}$ and side $MN=5\text{cm}$.

Step 1:
Draw the line segment MN of the length 5 cm.

Step 2:
Measure the angle M with your protractor. Make a mark at 90 degrees and draw a line MX from M passing through the mark.

Step 3:
Draw an arc with N as the centre and radius equal to $8cm$, such that it intersects MX.

Step 4:
Mark the point of intersection as L.

Step 5:
Join points L and N.

1. Construct a right angle XMN at M.
2. Construct an angle of 60 degrees XMN at M.
3. Above steps are sufficient to construct a right angle triangle
4. Construct an angle of 45 degrees at M.

Q.

A right triangle with the lengths of perpendicular sides 5 cm and 6 cm is constructed. Then, the length of the third side is

1. 7.2 cm

2. 6.6 cm

3. 7.8 cm

4. 8.2 cm

Q.

Construct a triangle, given that the lengths of its two sides are 3 m and 8 m and the third side makes an angle of 60 degrees with the 3 m side. [3 MARKS]

Q. Check if the following triangles can be constructed.

a) 80 cm, 5 cm, 5 cm

b) 13 cm, 6 cm, 7 cm [4 MARKS]

Q. A triangle ABC is constructed with BC = 5 cm, AB = 3 cm and $\angle A={90}^{\circ }$. Then, the correct classification of $\Delta$ ABC is

1. Based on sides - Scalene; Based on angle - Right angled
2. Based on sides - Isosceles; Based on angle - Acute angled
3. Based on sides - Scalene; Based on angle - Acute angled
4. Based on sides - Isosceles; Based on angle - Right angled

Q. Question 6
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.
$\begin{array}{ccccc}& Triangle& & Givenmeasurements& \\ 6.& \Delta PQR& PQ=3.5cm& QR=4cm& PR=3.5cm\end{array}$

Q. Construct a right triangle having hypotenuse of length 5.6 cm and one of whose acute angles measures 30°.

Q. Construct a right angle triangle whose perpendicular sides are 12 cm and 5 cm, using a ruler and a set square. Write its steps of construction. Also measure the length of the third side.

Q. A triangle ABC is constructed with AB = 5 cm, BC = 9 cm and $\angle A={90}^{\circ }$. Then, the length of third side is _______ cm.

1. 7.48

Q.

Construct $△NEW$ such that $\angle N=45°,NE=3.7cm$ and $NW=4.2$.

Q.

Construction of a triangle with the following specifications is possible.

Length of side AB = 8 cm, Length of side BC = 3 cm and $\angle$A = 40${}^{\circ }$.

1. True

2. False

Q. For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. Equilateral triangle
2. Right angled triangle
3. Scalene triangle
4. None of the above

Q. Question 3
Construct the following and give justification :

A right triangle when one side is 3.5cm and the sum of other sides and the hypotenuse is 5.5cm.

Q. A triangle ABC is constructed with AB = 5 cm, BC = 9 cm and $\angle A={90}^{\circ }$. Then, the length of third side is _____.

1. 6.98 cm
2. 7.48 cm
3. 6.42 cm
4. 8.24 cm

Q. Construct a ∆ABC in which BC = 5.8 cm, ∠B = ∠C = 30°. Measure AB and AC. What do you observe?

Q. The construction of a ∆ABC in which BC = 6 cm and ∠B = 50° is not possible when (AB − AC) is equal to
(a) 5.6 cm
(b) 5 cm
(c) 6 cm
(d) 4.8 cm