Easy Level Worksheet
Part A: Subjective Questions - Very Short Answer (1 Mark Each)
Note: Answer each question with steps and explanation. Draw constructions on your answer sheet and submit to the school subject teacher.
Triangle construction is an important skill in geometry. We can construct triangles using different given measurements.
Let's learn the basic requirements and conditions for constructing triangles.
1. What is required to construct a triangle?
To construct a triangle, we need
Perfect! We need three measurements like 3 sides, or 2 sides and 1 angle, etc.
2. How many measurements are needed to draw a unique triangle?
Answer:
Excellent! Three measurements ensure a unique triangle.
3. Name the instrument used to draw an arc.
Answer:
Correct! A compass is used to draw arcs and circles.
4. Write the full form of RHS in triangle construction.
RHS =
Great! RHS stands for Right angle, Hypotenuse, and Side.
5. What is the first step in constructing a triangle?
The first step is to
Perfect! We usually start by drawing the base of the triangle.
6. What is the angle sum property of a triangle?
Sum of all angles =
Excellent! The sum of all three angles in a triangle is always 180°.
7. Can a triangle be constructed if the sum of two sides is equal to the third side?
Correct! Sum of any two sides must be greater than the third side.
8. Write the condition for the possibility of triangle construction using three sides.
Sum of any two sides must be
Perfect! This is the triangle inequality property.
9. What is the base of a triangle?
The base is
Great! The base is usually the bottom side or the given side we draw first.
10. How many medians can be drawn in a triangle?
Answer:
Excellent! Each triangle has exactly 3 medians (from each vertex to opposite side).
Drag each condition to what it represents:
Part A: Section B – Short Answer Questions (2 Marks Each)
1. Construct a triangle with sides 5 cm, 6 cm, and 7 cm.
Draw this on your answer sheet:
Steps:
- Draw base BC =
cm
2. With B as center, draw arc of radius
3. With C as center, draw arc of radius
4. Mark intersection point as
5. Join A to B and A to C
Did you complete the construction?
Excellent! This is SSS (Side-Side-Side) construction.
2. Construct a triangle ABC in which BC = 5 cm, ∠B = 60°, and AB = 4 cm.
Steps:
1. Draw base BC =
2. At B, draw an angle of
3. On this ray, cut AB =
4. Join
Construction completed?
Perfect! This is SAS (Side-Angle-Side) construction.
3. Construct a right triangle whose base is 6 cm and hypotenuse is 10 cm.
Steps:
1. Draw base BC =
2. At B, draw a
3. With C as center, draw arc of radius
4. Mark intersection as
5. Join A to C
Construction completed?
Great! This is RHS (Right-Hypotenuse-Side) construction.
4. Construct a triangle with two sides 5 cm and 7 cm, and included angle 45°.
This is
Draw one side
Construction completed?
Perfect! You've used SAS condition correctly.
5. Construct an equilateral triangle of side 5 cm.
An equilateral triangle has all sides
Each angle in equilateral triangle =
Draw base 5 cm, then two arcs of
Construction completed?
Excellent! All sides are 5 cm and all angles are 60°.
Part B: Objective Questions - Test Your Knowledge!
Answer these multiple choice questions:
6. In a right triangle, the side opposite to the right angle is called:
(a) Base (b) Height (c) Hypotenuse (d) Median
Correct! The hypotenuse is the longest side opposite to the right angle.
7. An equilateral triangle has all sides:
(a) Unequal (b) Equal (c) Different (d) None
Perfect! Equilateral means all three sides are equal in length.
8. A triangle can be drawn if:
(a) Sum of two sides < third side
(b) Sum of two sides > third side
(c) One side = other
(d) None
Excellent! This is the triangle inequality property - essential for construction.
9. The number of medians in a triangle is:
(a) 2 (b) 3 (c) 4 (d) 6
Correct! A triangle has exactly 3 medians, one from each vertex.
10. The included angle in SAS stands for:
(a) Angle between equal sides
(b) Angle between given sides
(c) Angle at base
(d) Any angle
Perfect! In SAS, the included angle is the angle between the two given sides.
🎉 Fantastic Work! You've Mastered Basic Triangle Construction!
Here's what you learned:
Requirements for Triangle Construction:
- Need 3 measurements for unique triangle
- Can be: 3 sides, 2 sides + 1 angle, 2 angles + 1 side, etc.
Triangle Construction Conditions:
1. SSS (Side-Side-Side):
- All three sides are given
- Check: Sum of any two sides > third side
2. SAS (Side-Angle-Side):
- Two sides and the included angle
- Angle must be between the two given sides
3. ASA (Angle-Side-Angle):
- Two angles and the included side
- Side must be between the two given angles
4. RHS (Right-Hypotenuse-Side):
- Right angle, hypotenuse, and one other side
- Used only for right-angled triangles
Triangle Inequality Property:
- Sum of any two sides > third side
- Example: 3, 4, 5 → 3+4 > 5 , 3+5 > 4 , 4+5 > 3
- Cannot form triangle: 2, 3, 5 → 2+3 = 5
Important Properties:
- Sum of all angles = 180°
- Equilateral triangle: All sides equal, each angle = 60°
- Isosceles triangle: Two sides equal
- Scalene triangle: All sides different
- Right triangle: One angle = 90°
Construction Tools:
- Ruler: To draw and measure straight lines
- Compass: To draw arcs and circles
- Protractor: To measure and draw angles
- Pencil: For drawing
Basic Construction Steps (SSS Example):
- Draw the base (one side)
- From one end, draw arc with radius = second side
- From other end, draw arc with radius = third side
- Mark intersection point
- Join the points
Special Triangles:
- Equilateral: 3 equal sides, 3 equal angles (60° each)
- Isosceles: 2 equal sides, 2 equal angles
- Right-angled: One 90° angle, hypotenuse is longest side
Triangle construction is fundamental in geometry and has applications in engineering, architecture, and design!