RS Aggarwal 2019,2020 solution class 7 chapter 17 Construction Exercise 17B

Exercise 17B

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Question 1:

Construct a ∆ABC in which BC = 3.6 cm, AB = 5 cm and AC = 5.4 cm. Draw the perpendicular bisector of the side BC.

Answer 1:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{ 1}\text{. Draw a line segment (AB) of length 5 cm.}\\ \text{ 2}\text{. Draw an arc of radius 5}\text{.4 cm from the centre (A).}\\ \text{ 3}\text{. With B as the centre, draw another arc }\mathrm{of radius 3}\text{.6 cm, cutting the previous arc at C. }\\ \text{ 4}\text{. Join AC and BC}\text{.}\\ \text{ 5}\text{. Taking B as the centre and the radius more than half of BC, draw two arcs on both the sides of BC}\text{.}\\ \text{ 6}\text{. Similarly, taking C }\text{}\text{as the centre and the same radius, draw arcs on both the sides of BC, cutting the previous arcs at P and Q.}\\ \text{ 7. Join PQ. }\end{array} \\ \text{Then, PQ is the required perpendicuar bisector of BC, meeting BC at D.} \end{gathered}$$

Question 2:

Construct a ∆PQR in which QR = 6 cm, PQ = 4.4 cm and PR = 5.3 cm. Draw the bisector of ∠P.

Answer 2:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ 1. \text{Draw a line segment QR of length 6 cm}\text{.}\\ \text{2}\text{. Draw arcs of 4}\text{.4 cm and 5}\text{.3 cm from Q and R, respectively. They intersect at P.}\\ \text{3}\text{. Draw an arc of any radius from the centre (P), cutting PQ and PR at S and T, respectively.}\\ \text{4}\text{. With S as the centre and the radius more than half of ST, draw an arc}\text{ .}\\ \text{5. With T as the centre and the }\mathrm{same radius}, draw \mathrm{another} \mathrm{arc} \mathrm{cutting} \mathrm{the} \mathrm{previously} \mathrm{drawn} \mathrm{arc} \mathrm{at} \mathrm{X}.\\ \text{6. Join P and X}\text{.}\end{array} \\ \mathrm{Then}, \mathrm{PX} \mathrm{is} \mathrm{the} \mathrm{bisector} \mathrm{of} \angle \mathrm{P}. \end{gathered}$$

Question 3:

Construct an equilateral triangle each of whose sides measures 6.2 cm. Measure each of its angles.

Answer 3:

$\begin{array}{l}\text{Steps of construction:}\\ 1. \text{Draw AB of length 6}\text{.2 cm}\text{.}\\ \text{2}\text{. By taking the centres as A and B, draw equal arcs of 6}\text{.2 cm on the same side of AB, cutting each other at C}\text{.}\\ \text{3}\text{. Join AC and BC}\text{.}\\ \end{array}$

When we will measure angles of triangle using protractor then we find that all angles are equal to 60$°$

Question 4:

Construct a ∆ABC in which AB = AC = 4.8 cm and BC = 5.3 cm. Measure ∠B and ∠C. Draw AD ⊥ BC.

Answer 4:

$\begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw BC=5}\text{.3 cm}\\ \text{2}\text{. Draw an arc of radius 4}\text{.8 cm from the centre, B}\text{.}\\ 3. \text{Draw another arc of radius 4}\text{.8 cm from the centre, C}\text{.}\\ \text{4}\text{. Both of these arcs intersect at A}\text{.}\\ \text{5}\text{. Join AB and AC}\text{.}\\ \text{6}\text{. With A as the centre and any radius, draw an arc cutting BC at M and N. }\\ \\ \text{7}\text{. With M as the centre and the radius more than half of MN, draw an arc.}\\ \text{8. With N as the centre and the same radius, draw another arc cutting the previously drawn arc at P. }\\ \text{9. Join AP, cutting BC at D.}\\ \mathrm{Then}, AD\perp BC\end{array}$

Question 5:

Construct a ∆ABC in which AB = 3.8 cm, ∠A = 60° and AC = 5 cm.

Answer 5:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw AB of length 3}\text{.8 cm}\text{.}\\ \text{2}\text{. Draw ∠BAZ=60°}\\ \text{3}\text{. With the centre as A, cut ray AZ at 5 cm at C.}\\ \text{4 Join BC.}\end{array} \\ \text{Then, ABC is the required triangle.} \end{gathered}$$

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Question 6:

Construct a ∆ABC in which BC = 4.3 cm, ∠C = 45° and AC = 6 cm.

Answer 6:

$\begin{array}{l}\begin{array}{l}\begin{array}{l}\text{Steps of construction:}\\ \text{1. Draw AC= 6 cm}\end{array}\\ \text{2. }\mathrm{Draw} \angle \mathrm{ACZ}=45°\end{array}\\ 3. \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre}, \mathrm{cut} \mathrm{ray} \mathrm{BZ} \mathrm{at} 4.3 \mathrm{cm} \mathrm{at} \mathrm{point} \mathrm{B}.\\ \begin{array}{l}\text{4. Join AB.}\\ \mathrm{Then}, \mathrm{ABC} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{triangle}.\end{array}\end{array}$

Question 7:

Construct a ∆ABC in which AB = AC = 5.2 cm and ∠A = 120°. Draw AD ⊥ BC.

Answer 7:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw AB=5.2 cm}\\ \text{2}\text{. Draw ∠BAX=120° }\\ \text{3}\text{. With A as the centre, cut the ray AX at 5.3 cm at point C.}\\ \text{4}\text{. Join BC.}\\ \text{5}\text{. With A as the centre and any radius, draw an arc cutting BC at M and N}.\\ 6. \text{With M as the centre and the radius more than half of MN, draw an arc.}\\ \text{7}\text{. With N as the centre and the same radius as before, draw another arc cutting the previously drawn arc at P.}\\ 8. \mathrm{Join} \mathrm{AP} \mathrm{meeting} \mathrm{BC} \mathrm{at} \mathrm{D}.\end{array} \\ \therefore \mathrm{AD}\perp \mathrm{BC} \end{gathered}$$

Question 8:

Construct a ∆ABC in which BC = 6.2 cm, ∠B = 60° and ∠C = 45°.

Answer 8:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw BC=6.2 cm}\\ \text{2}\text{. Draw ∠BCX=45°}\\ \text{3}\text{. Draw ∠CBY=60°}\end{array} \\ 4.\mathrm{The} \mathrm{ray} \mathrm{CX} \mathrm{and} \mathrm{BY} \mathrm{intersect} \mathrm{at} \mathrm{A}. \\ \mathrm{Then}, \mathrm{ABC} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{triangle}. \end{gathered}$$

Question 9:

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

Answer 9:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw BC=5}\text{.8 cm}\end{array} \\ 2. \mathrm{Draw} \angle \mathrm{BCY}=30° \\ 3. \mathrm{Draw} \angle \mathrm{CBX}=30° \\ 4. \mathrm{The} \mathrm{ray} \mathrm{BX} \mathrm{and} \mathrm{CY} \mathrm{intersect} \mathrm{at} \mathrm{A}. \\ \mathrm{Then}, \mathrm{ABC} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{triangle}. \\ \mathrm{On} \mathrm{measuring} \mathrm{AB} \mathrm{and} \mathrm{AC}: \\ \mathrm{AB}=\mathrm{AC}=3.4 \mathrm{cm} \end{gathered}$$

Question 10:

Construct a ∆ABC in which AB = 7 cm, ∠A = 45° and ∠C = 75°.

Answer 10:

$$\begin{gathered} \mathrm{By} \mathrm{angle} \mathrm{sum} \mathrm{property}: \\ \angle B=180°-\angle A-\angle C \\ =180°-45°-75° \\ =60° \\ \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw AB=7cm}\\ \text{2 Draw ∠BAX= 45°}\\ 3. \text{Draw ∠ABY= 60°}\\ \text{4.The ray AX and BY intersect at C.}\end{array} \\ \text{Then, ABC is the required triangle.} \end{gathered}$$

Question 11:

Construct a ∆ABC in which BC = 4.8 cm, ∠C = 90° and AB = 6.3 cm.

Answer 11:

$\begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{.Draw BC=4}\text{.8 cm}\\ \text{2}\text{.Draw a perpendicular on C such that }\angle {\text{C is equal to 90°.}}^{}\\ 3.\text{Draw an arc of radius 6}\text{.3 cm from the centre B.}\\ 4.\text{Join AB.}\end{array}$

Question 12:

Construct a right-angled triangle one side of which measures 3.5 cm and the length of whose hypotenuse is 6 cm.

Answer 12:

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw AB=3}\text{.5 cm}\\ \text{2}\text{. Construct }\angle \text{ABX}=90°\\ 3. \mathrm{With} \mathrm{centre} \mathrm{A}, \mathrm{d}\text{raw an arc of radius 6 cm cutting BX at C.}\\ \text{4}\text{. Join AC.}\end{array} \\ \text{Then, ABC is the required triangle.} \end{gathered}$$

Question 13:

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

Answer 13:

$$\begin{gathered} \begin{array}{l}\text{Here, }\angle \text{A=30° and }\angle \text{C=90}°\\ \text{By angle sum property: }\\ \angle \text{B=60}°\end{array} \\ {\text{ 1. Draw the hypotenuse AB of length 5.6 cm.}}^{} \\ \text{2. Draw}\angle BAX=30° \mathrm{and} \angle ABY=60° \\ 3. \mathrm{The} \mathrm{ray} \mathrm{AX} \mathrm{and} \mathrm{BY} \mathrm{intersect} \mathrm{at} \mathrm{C}. \\ \mathrm{Then}, \mathrm{ABC} \mathrm{is} \mathrm{the} \mathrm{required} \mathrm{triangle}. \end{gathered}$$