ASA Triangle Construction

ASA Triangle Construction

To construct a triangle when two of its angles,say B and C, and the included side BC are given,we proceed as follows :

Step 1 : Draw a line segment BC.

Step 2 : Draw ∠CBX of measure equal to that of ∠B.

Step 3 : Draw ∠BCY with Y on the same side of BC as X, such that its measure is equal to that of ∠C. Let BX and CY intersect at A. Then, ΔABC is the required triangle. Example

Construct a ΔABC in which BC = 6 cm, ∠B = 35
0 and ∠C = 100 0 .

Step 1 : Draw a line segment BC = 6 cm.

Step 2 : Draw ∠CBX, such that ∠CBX = 35
0

Step 3 : Draw ∠BCY with Y on the same side of BC as X such that
∠BCY = 100
0

Step 4 : Let BX and CY intersect at A.

ΔABC is the required triangle. ________________________________________________________________

Practice Problems

1) If we have PQ = 5 cm, ∠PQR= 115° and ∠QRP = 30°, can we construct a ΔPQR with these measurements?

2) State true or false: In ΔABC, the side included between ∠B and ∠C is AB.

3) Construct ΔABC in which BC=6 cm, ∠B = 35
0 and ∠C = 100 0 .
Measure ∠A.

4) In ΔABC, BC = CA. Which of its two angles are equal ?

5) If m∠A=70
0 ,AB= 5cm and m∠B=60 0 which rule is used here to construct triangle ABC?
Geometrical Constructions

Basic Geometric Constructions
Construction of Line Segment
Bisecting a Line Segment
Constructing Angles
Bisecting Angles
Constructing Parallel Lines
Construction of Triangle (SSS)
SAS Triangle Construction
ASA Triangle Construction
HL Triangle Construction (Rhs -construction)