# HL Triangle Construction

**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 90

^{0}.

**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 = 90

^{0}, PR = 6 cm and QR = 4 cm.

Step 1: Draw QR = 4 cm.

Step 2 : Using compass, at Q draw ∠RQK = 90

^{0}.

Step 3 : Cut off RP = 6 cm.

Step 4 : Join P and R.

Now we get the required ΔPQR.

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**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 = 90

^{0}.

3) In a triangle PQR, if ∠P=90

^{0}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)

• 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)