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Isosceles Triangles

Theory & Practice Questions.

Lesson

[Definition]

Isosceles Triangles

An isosceles triangle has two equal sides and two equal base angles

isosceles triangle

 

Example

Match the numbered statements in Column X with the letters allocated to the diagrams in Column Y by classifying according to sides or angles.
Explain your answers.

 

Column X

 

Column Y

1

  An acute triangle has 3 acute angles

A

a right angled triangle
2

A right triangle has 1 right angle

B
obtuse triangle
3

An obtuse triangle has 1 obtuse angle

C
equilateral triangle
4

  An equilateral triangle has 3 congruent sides  

D
scalene triangle
5

  An isosceles triangle has at least 2 congruent sides  

E
an acute triangle
6

A scalene triangle has no sides of equal length

F
an isosceles triangle

 

 

Solution

  1-E

  All angles are less than 90° 

  2-A

  One angles is equal to 90° 

  3-B

  One angle is greater than 90° 

  4-C

 All sides are of equal length

  5-F

  Two sides are of equal length

  6-D

  None of the sides are equal length  

 

 

Question

A triangle’s largest angle is 2.5 times larger than the smallest angle. If the third angle is 40°, what type of triangle is it?

 

Explanation

Given the information, we can create an equation and solve.

2.5x + x +40 = 180

3.5x = 140

x = 40

Therefore, the angles are 100°, 40°, 40° and the triangle is isosceles.

 

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