CONSTRUCTION OF TRIANGLES: SIMPLE CASES
Construction: To construct a triangle, when its three sides are given.
Example: To construct ?ABC in which
AB = 4 cm, BC = 5 cm, CA = 3.5 cm.
Steps of Construction:
1. Draw BC = 5 cm.
2. With centre B and radius 4 cm (= AB) draw an are, one side of BC.
3. With centre C, and radius 3.5 cm (=AC) draw another are, intersecting the arc of step 2 in A.
4. Join AB and AC.
Then MBC is the required triangle.
Construction: To construct a triangle when two of its sides and the included angle are given.
Example: Construct ?ABC, where AB = 2.5 cm, BC = 3 cm and
?B = 60°
Steps of Construction:
1. Draw BC = 3 cm.
2. Draw ray BY, such that ?CBY = 60°.
3. From BY, cut off BA = 2.5 cm.
4. Join AC.
Then, ?ABC is the required triangle.
Construction: To construct a right triangle whose hypotenuse and one side are given.
Example: Construct a right triangle ABC, right angled at C, in which hypotenuse AB = 5.5 cm and one side BC = 4.5 cm.
Steps of Construction:
1. Draw BC = 4.5 cm.
2. At C, draw ray CY, such that ?BCY = 90°.
3. With centre B and radius 5.5 cm (= AB), draw an arc intersecting CY in A.
4. Join AB.
Then MBC is the required triangle.
Construction: To construct a triangle, given three medians.
Example: Construct ?ABC, in which its medians AD = 3.9 cm, BE = 4.5 cm and CF = 5.4 cm.
Solution: Let G be the centroid.
We know that G divides the medians in the ratio 2: 1.
AG = 2/3 × AD = 2/3 × 3.9 = 2 6 cm = GH
BG= 2/3× BE=2/3×4.5=3.0 cm=CH
CG= 2/3×CF=2/3×5.4 =3.6 cm= BH
? Construct ||gm BGCH and complete ?ABC as under:
Steps of Construction:
1. Draw ?BGH with BG = 3 cm and BH = 3.6 cm and GH = 2.6 cm.
2. Complete ||gm BGCHss.
3. Join HG and produce it to A so that AG = GH = 2.6 cm.
4. Join AB, AC and BC.
Then MBC is the required triangle.
Construction: To divide a given line segment into a number of equal parts.
Steps of Construction:
1. Draw ray AY, making any acute ?BAY.
2. On AY, starting from A, locate points A1, 2’ A3, A4 and A5 such that
AA1 = A1A2 = A2A3 = AA4 = A4A5
3. Join A5B.
4. Through A4, A3, A2, A1 draw lines parallel to A5B, intersecting AB in P4, P3, P2 and P1 respectively. Then, points P1 P2, P3, P4 are the required points dividing AB into 5 equal parts, AP1 P1P2, P2P3, P3P4 and P4P5.
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