Construction Of Triangle Similar To A Given Triangle

Construction of Triangle Similar to a Given Triangle Example 1: Construct a triangle ABC of sides 3 cm, 4 cm and 5 cm. Draw a triangle A' B 'C ' similar to Triangle ABC , each of whose side is 2 of the 3 corresponding sides of Triangle ABC . Solution: Steps of construction

1. Take a line segment BC of length 4 cm. With B and C as respective centers and radii 3 cm and 5 cm, draw two arcs intersecting each other at A. Join AB and AC. This constructs Triangle ABC .

2. On the opposite side of vertex A, draw an acute angle CBX. 3. On BX, mark points B1 , B2 , B3 such that BB1 = B1 B2 = B2 B3 . Join B3C . 4. From B2 draw B2C ' parallel to B3C by making corresponding angles equals intersecting BC in C ' 5. From C ' draw C ' A parallel to CA as before, intersecting AB in A' . Now A' B 'C ' is the required triangle. Example 2: Construct a Triangle ABC whose sides are 8 cm, 7 cm and 6 cm. Construct another triangle to Triangle ABC and with sides 2 rd of the 3 corresponding sides of Triangle ABC . Solution:

Steps of construction

1. Draw Triangle ABC with ruler and compasses. 2. Divide the base AB into three equal parts. Let B ' be the point on AB such that 2 A' B ' = AB 3 3. Draw a line B 'C ' parallel to BC intersecting AC at C ' . Then Triangle A' B 'C ' is the required triangle. Example 3: Construct a triangle similar to given triangle with sides 3 cm, 4 cm, 7 and 5 cm whose sides are th of the corresponding sides of the given triangle. 5 Solution:

Steps of construction

1. Draw the given triangle ABC. 2. At A, draw a ray AX inclined at a certain angle with AB on opposite side of C. 3. Starting from A, cut off seven AX 1 , X 1 X 2 , X 2 X 3 , X 3 X 4 , X 4 X 5 , X 5 X 6 , X 6 X 7 on AX.

equal

line

segments

4. Join BX 5 and draw a line X 7 B ' parallel to X 5 B to intersect AB produced at B ' . 5. Draw a line B 'C parallel to BC to intersect AC produced at C ' . Now Triangle A' B 'C ' is the required triangle. Example 4; Construct a triangle XYZ of sides 5 cm, 6 cm, and 7 cm. construct 7 another Triangle X 'Y ' Z ' whose sides are th of the corresponding sides of the 5 Triangle XYZ . Solution:

Steps of construction 1. Take a line segment of length 5 cm. With Y and Z as respective centers and radii 6 cm and 7 cm draw two arcs intersecting each other at X. Join XY and XZ. Now, Triangle XYZ is the triangle with sides 5 cm, 6 cm and 7 cm. 2. On the other side of YZ in which vertex X lies, draw an acute angle ZYA. On YA, mark seven points Y1 , Y2 , Y3 , Y4 , Y5 , Y6 , Y7 such that YY1 = Y1Y2 = Y2Y3 = Y3Y4 = Y4Y5 = Y5Y6 = Y6Y7 . Join Y5 to Z. 3. From Y7 , draw Y7 Z ' parallel to Y5 Z , intersecting YZ produced in X. 4. From Z ' draw Z ' X ' parallel to ZX , meeting YZ produced in X ' . Now Triangle X 'Y ' Z ' is the required triangle.

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