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Properties of Geometric Figures, SM-Bank 011

In the diagram, \(AB\) is parallel to \(DE\).
 

  1. On the diagram, label the alternate angles to \(a^{\circ}\) and \(b^{\circ}\).   (1 mark)

  2. Using part (a), show that the sum of internal angles of a triangle equals 180°.   (2 marks)
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a.    
     

b.    \(DE\ \text{is a straight line.}\)

\(a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\ \ \text{(180° in a straight line)}\)

\(\therefore \ \text{Angle sum of}\ \Delta = a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\)

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a.    
       

b.    \(DE\ \text{is a straight line.}\)

\(a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\ \ \text{(180° in a straight line)}\)

\(\therefore \ \text{Angle sum of}\ \Delta = a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\)

Properties of Geometrical Figures, SM-Bank 017

The diagram below shows an isosceles triangle.
 

Determine the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)

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\(40^{\circ}\)

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\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)

\(x^{\circ}\) \(=180-(2 \times 70)\ \ \text{(180° in triangle)} \)  
  \(=180-140\)  
  \(=40^{\circ}\)  

Properties of Geometrical Figures, SM-Bank 016

The diagram below shows an isosceles triangle.
 

Determine the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)

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\(110^{\circ}\)

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\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)

\(x^{\circ}\) \(=180-(2 \times 35)\ \ \text{(180° in triangle)} \)  
  \(=110^{\circ}\)  

Properties of Geometrical Figures, SM-Bank 015

The diagram below shows an isosceles triangle.
 

Determine the value of \(a^{\circ}\), giving reasons for your answer.   (2 marks)

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\(71^{\circ}\)

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\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)

\(2a^{\circ}\) \(=180-38\ \ \text{(180° in triangle)} \)  
\(a^{\circ}\) \(=\dfrac{142}{2}\)  
  \(=71^{\circ}\)  

Properties of Geometrical Figures, SM-Bank 014

The diagram below shows an isosceles triangle.
 

Determine the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)

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\(59^{\circ}\)

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\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)

\(2x^{\circ}\) \(=180-62\ \ \text{(180° in triangle)} \)  
\(x^{\circ}\) \(=\dfrac{118}{2}\)  
  \(=59^{\circ}\)  

Properties of Geometrical Figures, SM-Bank 004 MC

A triangle is divided into 2 parts by a straight line.

The angles are then labelled.
 

Which statement is true about the sum of angles?

  1. `b + c + d = 180^@`
  2. `c + d + e = 360^@`
  3. `a + b + f + g = 360^@`
  4. `d + e + f + g = 180^@`
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`C`

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`text(Consider each option:)`

`text(Option A:)\ \ b + c + d != 180\ \ => \ b+c = 180^@`

`text(Option B:)\ \ c + d + e != 360^@\ \ => \ c + d + e = 180^@\ \ text{(angle sum of triangle)}`

`text(Option C:)\ \ a + b + f + g = 360^@`

  `=>\ text(Correct since the angle sum of a quadrilateral = 360°)`

`text(Option D:)\ \ d + e + f + g != 180\ \ => \ e + f  = 180^@`

`=> C`