# 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.

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**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)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

• 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)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)