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Construct Trianglepqr If Pq = 5 Cm, M∠Pqr = 105° and M∠Qrp = 40°. (Hint: Recall Angle Sum Property of a Triangle). - CBSE Class 7 - Mathematics

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ConceptConstructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)

Question

Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°. (Hint: Recall angle sum property of a triangle).

Solution

A rough sketch of the required ΔPQR is as follows.

In order to construct ΔPQR, the measure of ∠RPQ has to be calculated.

According to the angle sum property of triangles,

∠PQR + ∠PRQ + ∠RPQ = 180º

105º + 40º + ∠RPQ = 180º

145º + ∠RPQ = 180º

∠RPQ = 180° − 145° = 35°

The steps of construction are as follows.

1) Draw a line segment PQ of length 5 cm.

2) At P, draw a ray PX making an angle of 35º with PQ.

3) At point Q, draw a ray QY making an angle of 105º with PQ.

4) Point R has to lie on both the rays, PX and QY. Therefore, R is the point of intersection of these two rays.

This is the required triangle PQR.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics for Class 7 (2018 to Current)
Chapter 10: Practical Geometry
Ex. 10.40 | Q: 2 | Page no. 202
Solution Construct Trianglepqr If Pq = 5 Cm, M∠Pqr = 105° and M∠Qrp = 40°. (Hint: Recall Angle Sum Property of a Triangle). Concept: Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion).
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