Question

question three - geometry of 2d shapes 10 marks
3.1. name the following triangles:
3.1.1.
3.1.2.
(1)
(1)
3.2. study the diagram below and identify three pairs of congruent shapes: (3)
3.2.1
3.2.2
3.2.3
3.3. examine the shapes below and answer the questions that follow:
(3)
3.3.1. are these rectangles similar?
(1)
3.3.2. provide two reasons for your answer:
(2)

Explanation:

3.1.1

Step1: Analyze triangle sides

All three sides are equal (marked with same tick marks).

3.1.2

Step1: Analyze triangle sides

Two sides are equal (marked with same tick marks).

3.2

Step1: Compare shapes

Check for same shape and size.

• \(A\) and \(C\) are both squares.
• \(E\) and \(F\) are both rectangles.
• \(H\) and \(G\) are both pentagons.

3.3.1

Step1: Calculate side ratios

For the smaller rectangle: length \(l_1 = 3\) cm, width \(w_1=2\) cm. For the larger rectangle: length \(l_2 = 9\) cm, width \(w_2 = 6\) cm.
\(\frac{l_2}{l_1}=\frac{9}{3}=3\), \(\frac{w_2}{w_1}=\frac{6}{2}=3\)

3.3.2

Step1: State similarity criteria

• Corresponding angles are equal (all angles in rectangles are \(90^{\circ}\)).
• Corresponding sides are in proportion (\(\frac{9}{3}=\frac{6}{2} = 3\)).

Answer:

3.1.1 Equilateral triangle
3.1.2 Isosceles triangle
3.2.1 \(A\) and \(C\)
3.2.2 \(E\) and \(F\)
3.2.3 \(H\) and \(G\)
3.3.1 Yes
3.3.2

• All corresponding angles are equal (\(90^{\circ}\)).
• Corresponding sides are in proportion (\(\frac{9}{3}=\frac{6}{2}=3\)).