Question

Can you construct a triangle if it's perimeter, base and the angles which include the base are given.

A) Yes

B) No

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Answer 1

Step-by-step explanation:

yes in this article we are going to discuss how to construct a triangle when its perimeter and its two angles are given

Answer 2

Answer:

yes

Step-by-step explanation:

Below are the steps to construct a triangle ABC when its perimeter (i.e. AB + BC + CA) and two base angles B and C are given.

Given: The Perimeter (AB + BC + CA) of the triangle and two angles (i.e. ∠B and ∠C).

Requirements: A ruler, a protractor and a compass.

Steps of Construction:

Step 1: Draw a line segment XY such that XY = AB + BC + CA (i.e. perimeter of triangle ABC) and draw the angle lines at X and Y such that ∠LXY = ∠B and ∠MYX = ∠C.

Step 2: Draw the angle bisectors of ∠LXY and ∠MYX and let them meet at A.

Step 3: Now, draw the perpendicular bisectors of AX and AY such that they intersect XY at B and C respectively. Join AB and AC.

Hence, this is the required triangle ABC.