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6. Construction of a triangle when its base, vertical angle and altitude are given

Let us learn how to construct a triangle with an example when its base, vertical angle and altitude from the vertex to the base are given.

Example:

Construct a

$\triangle ABC$ such that

$AB = 5 \ cm$ ,

$\angle C = 45^{\circ}$ , and the altitude from

$C$ to

$AB$ is of length

$2 \ cm$ .

Solution:

First, let us draw a rough figure.

Construction:

Step 1: Draw a line segment

$AB$ of length

$5 \ cm$ .

Step 2: At

$A$ , draw

$AE$ such that

$\angle BAE = 45^{\circ}$ .

Step 3: At

$A$ , draw

$AD$ such that

$\angle EAD = 90^{\circ}$ .

Step 4: Draw the perpendicular bisector

$XY$ to

$AB$ , which intersects

$AD$ at

$G$ and

$AB$ at

$F$ .

Step 5: With

$G$ as centre and

$GA$ as radius, draw a circle

$ABH$ .

Step 6: From

$F$ , mark an arc in the line

$XY$ at

$I$ , such that

$FI = 2 \ cm$ .

Step 7: Draw

$NM$ through

$I$ , which is parallel to

$AB$ .

Step 8:

$NM$ meets the circle at

$A$ and

$J$ .

Step 9: Join

$AB$ and

$AC$ . Thus,

$ABC$ is the required triangle.

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6. Construction of a triangle when its base, vertical angle and altitude are given

Theory: