#### How to draw the Angle Side Angle triangles? Properties of Angle Side Angle triangle construction.

Angle Side Angle (ASA) Triangle Congruence

The sum of the three angles of a triangle is 180°. To be able to construct a triangle using ASA we must know the angle at each end of the given line segment. If one of these is not given then we must calculate it from the other two angles by subtracting their sum from 180°.

Example- Construct triangle ABC in which mA = 50°, b = 5 cm and mB = 60°.

Since we are not given the angles on each end of the given side, [AC], we must first calculate mC.

$\displaystyle m\overset{\wedge }{\mathop{C}}\,=180{}^\circ -\left( m\overset{\wedge }{\mathop{A}}\,+m\overset{\wedge }{\mathop{B}}\, \right)$

$\displaystyle \Rightarrow m\overset{\wedge }{\mathop{C}}\,=180{}^\circ -\left( 50{}^\circ +60{}^\circ \right)$

$\displaystyle \Rightarrow m\overset{\wedge }{\mathop{C}}\,=70{}^\circ$

(a) Draw a sketch diagram and mark the three elements that will be used in the construction.

(b) Draw a line segment [CA] of length 5 cm.

(c) Measure C and draw a ray from C at 70° to [CA.

(d) Measure A and draw a ray from A at 50° to [AC.

(e) Mark B, the point of intersection of these two rays.