Practical geometry class 7 notes are provided here which can help the class 7 students to learn this chapter in a better and more effective way. These CBSE maths chapter 10 notes are concise and students can not only learn the topics but can also revise the concepts easily. The main topics from this chapter that are included here are-

- Introduction to practical geometry
- Constructions using only ruler and compass
- Construction of triangles with SSS, SAS, ASA, and RHS criterion
- Example Questions
- Related Articles

## Introduction to Class 7 Practical Geometry

In this chapter, students learn how to construct different shapes i.e. lines and triangles using only a ruler and a compass. For construction of triangles, students learn how to construct triangles when-

- Measurement of 3 sides is given (SSS)
- Measurement of 2 sides an angle between them is given (SAS)
- Measurement of 2 angles and of the side between them is given (ASA)
- Length of hypotenuse and the length of one of its sides are given for a right-triangle (RHS)

### Construction of Two Parallel Lines Using Ruler and Compass

**Steps 1: **Draw any line “l” and take a point “A” outside that line. Also, select a point “B” on that line and join point A and point B.

**Step 2: **From point B, draw and arc cutting line BA and BL. Mark the “D” and “C” respectively.

**Step 3: **From A, draw the arc of same radius from A.

**Step 4: **Take the distance CD using the compass and cut the arc FGE at both sides from G.

**Step 5: **Draw a straight line which touches both H and A.

In this, line “m” and line “n” are parallel since angle ABC and angle BAH are alternate interior angles.

### Construction of Triangles

**SSS: **in this, the length of three sides of the triangle are given.

**Step 1: **To draw a triangle ABC with the given lengths, draw a line BC of the given length using a ruler.

**Step 2: **From point B, draw an arc according to the length of BA above the line BC. Then, from point C, draw another arc according to the given length CA.

**Step 3: **Name this point as A and join the lines.

**SAS: **In this, the measurement of two sides and the angle between them is given. An example is given below for better understanding.

**Example:**

Construct a triangle PQR with PQ = 3 cm, QR = 5.5 cm and angle PQR = 60 degrees.

**Step 1: **Draw a QR of length 5.5 cm

**Step 2: **From Q, draw QX such that it is making 60 degrees with QR. Then, measure 3 cm from Q on the line QX and mark that point as P. Then by joining P and R, the desired triangle is ready.

**ASA: **In this, the degrees of two angles are given and the length of the side between them are given.

**Example:**

Construct a triangle XYZ with XY = 6 cm, angle ZXY = 30° and angle XYZ = 100°.

**Step 1: **Draw a line segment XY of length 6 cm.

**Step 2: **Draw XP which is making an angle of 30 degrees from XY and YQ which is making an angle of 100 degrees from XY.

**Step 3: **Join the lines XP and YQ by converging and mark the point as Z. Triangle XYZ is then constructed using the parameters given.

**RHS: **In this type, length of one leg and its hypotenuse are given. An example of the construction using this criterion is given below.

**Example: **Construct a triangle LMN which is right angles at M and the length of LN and MN are 5 cm and 3 cm respectively.

**Step 1: **Draw MN having the length of 3 cm and from M, draw a line MX which is perpendicular to MN.

**Step 2: **From M, draw an arc of 5 cm on MX and name it L. Now, from L, draw a line segment till N. Now, the triangle LMN is constructed using the given criteria.

### Example Questions

- Construct a right angled triangle ABC, where angle B = 90°, BC = 8cm and AC = 10 cm.
- Construct an isosceles triangle which has two equal sides of lengths 6.5 cm each and have an angle of 110 degrees between them.
- Construct a triangle ABC with AB = 4 cm, BC = 3.5 cm and AC = 4 cm. Also, mention the type of triangle it forms?

### Related Articles

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