# HL Triangle Construction

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HL Triangle Construction (RHS triangle Construction) : A triangle is said to be a right triangle, if one of its three angles is a right angle. To construct a right triangle ABC right angled at C when its hypotenuse is AC and one side is BC is given, we follow the following steps :

Step 1 : Draw a line segment BC of given length.

Step 2: Draw ∠BCX of measure 900.

Step 3 : With center B and radius equal to the hypotenuse AB, draw an arc of the circle to intersect ray CX at A.

Step 4 : Join BA to obtain the required triangle ABC. Example

RHS Triangle Construction

Construct a right triangle PQR in which ∠Q = 900, PR = 6 cm and QR = 4 cm.

Step 1: Draw QR = 4 cm.

Step 2 : Using compass, at Q draw ∠RQK = 900.

Step 3 : Cut off RP = 6 cm.

Step 4 : Join P and R.

Now we get the required ΔPQR. ________________________________________________________________
Practice Problems

1) If the sides of triangle are 3cm,4cm and 5cm then what type of triangle you will get after constructing it?

2) Construct a right angled triangle ABC where AB = 4.5 cm, AC = 5.8 cm and angle A = 900.

3) In a triangle PQR, if ∠P=900 and ∠Q= ∠R, find the angles of the triangle .

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)