Moderate Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

In this moderate level, we'll explore detailed construction steps, verify triangle properties, and understand why some triangles cannot be constructed.

Let's deepen our understanding of construction conditions and triangle properties.

1. Write the construction condition when three sides of a triangle are known.

Construction condition: SSS (Side-Side-Side)SAS

Perfect! When all three sides are known, we use SSS condition.

2. Name the triangle construction rule used when two angles and included side are given.

Answer: ASA (Angle-Side-Angle)SAS

Excellent! ASA is used when two angles and the side between them are given.

3. Write the steps of construction under SAS condition.

Step 1: Draw the basefirst side

Step 2: Draw the included angleany angle at one end

Step 3: Cut the second sidethird side on the ray

Step 4: Join to complete the triangleshape

Great! These are the key steps for SAS construction.

4. What are the possible sets of data to draw a triangle uniquely?

Valid conditions: , , ,

Perfect! These four conditions ensure unique triangle construction.

5. Can a triangle be constructed with sides 3 cm, 4 cm, and 8 cm? Why?

NoYes, because 3 + 4 = which is less thangreater than 8

Correct! This violates the triangle inequality property (sum of two sides must be > third side).

6. Which property ensures the possibility of triangle construction?

Answer: Triangle inequality propertyAngle sum property

Excellent! This property must be checked before attempting construction.

7. Name the triangle construction condition used for right triangles.

Answer: RHS (Right-Hypotenuse-Side)ASA

Perfect! RHS is specifically for right-angled triangles.

8. Which condition is not valid for triangle construction? (SSA or SAS)

SSASAS is not valid because it doesn't give a uniqueproper triangle

Correct! SSA (Side-Side-Angle) can give two different triangles or no triangle.

9. What is the sum of angles in a triangle?

Sum of angles = °

Great! This is the angle sum property of triangles.

10. Which tools are needed to construct a triangle?

Tools needed: , ,

Excellent! These are the essential geometric tools for construction.

Drag each step sequence to its construction condition:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Construct ΔABC with AB = 5 cm, AC = 6 cm, and BC = 7 cm.

Draw on your answer sheet.

Check triangle inequality: 5 + 6 = > 7

This is construction.

Draw BC = cm as base

From B, arc of radius cm; from C, arc of radius cm

Mark intersection as

Construction completed? YesDone

Excellent! ΔABC is constructed using SSS condition.

2. Construct a triangle ABC given that AB = 4 cm, ∠A = 50°, and AC = 5 cm.

This is construction (two sides and includedany angle)

Draw AB = cm

At A, draw angle °

On ray, cut AC = cm

Join to

Construction completed? YesDone

Perfect! You've used SAS condition correctly.

3. Construct a right triangle ABC, where AB = 6 cm and hypotenuse AC = 10 cm.

Check: AC² = AB² + BC²

10² = 6² + BC² → BC² = - =

So BC = cm

This is construction

Draw AB = 6 cm, make ° at B, arc from A with radius cm

Construction completed? YesDone

Excellent! This is a 6-8-10 right triangle (Pythagorean triplet).

4. Construct a triangle with sides 4 cm, 5 cm, and 6 cm.

Check: 4 + 5 = > 6

This is construction

Largest side cm should be the base

Draw arcs of cm and cm from the ends

Construction completed? YesDone

Great! This forms a scalene triangle.

5. Construct an isosceles triangle whose equal sides are 5 cm each and base 4 cm.

Isosceles means two sides equalall sides equal

Draw base = cm

From both ends, draw arcs of radius cm

Mark intersection and join to form triangle

Construction completed? YesDone

Perfect! The two equal sides and two equal angles confirm it's isosceles.

Part A: Section C – Long Answer Questions (4 Marks Each)

1. Construct ΔABC where AB = 5 cm, AC = 6 cm, and ∠A = 50°.

(a) Write steps of construction:

Step 1: Draw AB = cm

Step 2: At A, construct angle °

Step 3: On the ray from A, cut AC = cm

Step 4: Join and

Step 5: ΔABC is complete

(b) Verify the triangle:

This is construction

Measure BC with ruler (approximately cm)

Measure ∠B and ∠C with protractor (should sum to °)

Construction completed? YesDone

Excellent! Triangle verified successfully.

2. Construct ΔPQR such that PQ = 5 cm, ∠Q = 60°, and PR = 6 cm.

Note: This needs careful analysis!

(a) Explain each step:

Given: PQ = 5 cm, ∠Q = 60°, PR = 6 cm

This is NOT standard SAS because angle at is given but is opposite to Q

Draw PQ = cm

At Q, make angle °

From P, draw arc of radius cm to intersect the ray at R

(b) Mention the construction condition:

This uses a combination approach

Construction completed? YesDone

Good work! This required understanding of multiple construction principles.

3. Construct a right triangle ABC in which base BC = 8 cm and hypotenuse AC = 10 cm.

(a) Steps of construction:

Step 1: Draw BC = cm

Step 2: At B, construct a ° angle (perpendicular)

Step 3: With C as center, draw arc of radius cm

Step 4: Mark intersection point as

Step 5: Join A to C

(b) Name the rule used:

Rule:

AB should measure cm (from Pythagoras: 10² = 8² + 6²)

Construction completed? YesDone

Perfect! This is a 6-8-10 Pythagorean triplet.

4. Construct a triangle whose sides are 5 cm, 7 cm, and 8 cm.

(a) Steps of construction:

Verify triangle inequality:

5 + 7 = > 8

5 + 8 = > 7

7 + 8 = > 5

Construction possible:

Draw base = cm (largest side)

Arc from left end = cm or cm

Arc from right end = the remaining measurement

Join to complete triangle

(b) Verify the triangle inequality property:

All three checks passed

Construction completed? YesDone

Excellent! Triangle inequality verified and construction complete.

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. The side opposite the right angle is:

(a) Base (b) Hypotenuse (c) Height (d) Median

Correct! The hypotenuse is always the longest side in a right triangle.

7. Which of the following cannot form a triangle?

(a) 4 cm, 5 cm, 6 cm

(b) 2 cm, 3 cm, 5 cm

(c) 3 cm, 4 cm, 5 cm

(d) 5 cm, 5 cm, 5 cm

Perfect! 2 + 3 = 5 (not greater than 5), so triangle inequality fails.

8. To draw a triangle, which instrument is not required?

(a) Ruler (b) Compass (c) Divider (d) Calculator

Correct! Calculator is not a geometric construction tool.

9. The first step in constructing ΔABC with given sides is:

(a) Draw base (b) Draw circle (c) Draw altitude (d) Measure height

Excellent! We always start by drawing the base (one side).

10. For ASA construction, we must know:

(a) Two sides and included angle

(b) Two angles and included side

(c) All sides

(d) One side and one angle

Perfect! ASA requires two angles with the side between them.

🎉 Outstanding Work! You've Mastered Intermediate Triangle Construction!

Here's what you learned:

• Detailed Construction Steps:

  SSS (Side-Side-Side):

  1. Draw the longest side as base
  2. From one end, draw arc with radius = second side
  3. From other end, draw arc with radius = third side
  4. Mark intersection point
  5. Join to complete triangle

  SAS (Side-Angle-Side):

  1. Draw one side
  2. At one end, construct the given angle
  3. On the ray, mark the second side length
  4. Join to complete triangle

  ASA (Angle-Side-Angle):

  1. Draw the given side
  2. At both ends, construct the given angles
  3. Extend rays until they intersect
  4. Triangle is complete

  RHS (Right-Hypotenuse-Side):

  1. Draw one side (base)
  2. At one end, construct 90° angle
  3. From other end, draw arc with radius = hypotenuse
  4. Mark intersection on perpendicular
  5. Join to complete triangle

• Triangle Inequality - Critical Check:

  • Before constructing, verify: Sum of any two sides > third side
  • Examples:
    • Can construct: 4, 5, 6 → 4+5=9 > 6
    • Cannot construct: 2, 3, 5 → 2+3=5 = 5
    • Cannot construct: 1, 2, 4 → 1+2=3 < 4

• Special Triangles and Properties:

  Equilateral Triangle:

  • All sides equal
  • All angles = 60°
  • Very symmetric

  Isosceles Triangle:

  • Two sides equal
  • Two angles equal (opposite to equal sides)
  • One line of symmetry

  Right Triangle:

  • One 90° angle
  • Pythagorean theorem: a² + b² = c² (c = hypotenuse)
  • Common triplets: 3-4-5, 6-8-10, 5-12-13

• Why SSA Doesn't Work:

  • SSA (Side-Side-Angle) is NOT a valid condition
  • Can produce two different triangles or no triangle
  • The angle must be included (between the sides) for uniqueness

• Angle Sum Property:

  • Sum of all three angles = 180°
  • If two angles known, third = 180° - (sum of other two)
  • Helps verify construction accuracy

• Tools and Their Uses:

  • Ruler: Drawing and measuring straight lines
  • Compass: Drawing arcs and circles, transferring lengths
  • Protractor: Measuring and constructing angles
  • Set Square: Drawing perpendiculars (90° angles)

• Verification Methods:

  1. Measure all sides with ruler
  2. Measure all angles with protractor
  3. Check: All angles sum to 180°
  4. Check: Triangle inequality holds
  5. For right triangles: Verify Pythagoras theorem

• Common Mistakes to Avoid:

  • Not checking triangle inequality first
  • Using wrong construction condition
  • Inaccurate angle measurement
  • Light construction lines (use sharp pencil)
  • Not labeling vertices clearly

Accurate triangle construction requires practice, patience, and proper use of geometric tools!