Geometry

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In today’s Mathematics class, We will be looking Geometry. We hope you enjoy the class!

 

Geometry

Similar Triangles

One of the following conditions is sufficient to show that two triangles are similar.

1. If two angle of one triangle is equal to two angles of the other.
2. If two pairs of sides are in the same ration and their included angles are the same.
3. If the ratios of the corresponding sides are equal.

 

Example

Show that ∆ABC and ∆XYZ as shown below are similar and hence find sides AB and XZ.

Solution

In ∆ABC:

< A = 180 – (32 + 38)

= 110⁰ 

Similarly, in ∆XYZ

<Z = 180⁰ – (110⁰ + 32⁰)

= 38⁰
<A = <x = 110⁰ , < B = <Y = 32⁰ and

<c = <z = 38⁰

Therefore, Triangles ABC and XYZ are similar because they are equiangular

Hence:    $\frac{AB}{XZ} = \frac{AC}{ZY} = \frac{BC}{YZ}$

 

Substituting the given sides:

$$\begin{gathered} \frac{AB}{2} = \frac{25}{XZ} = \frac{35}{7} \\ Hence: \frac{AB}{2} = \frac{35}{7} and \frac{25}{XZ} = \frac{35}{7} \\ \frac{AB}{2} = \frac{35}{7} and \frac{25}{XZ} = \frac{35}{7} \\ \frac{AB}{2} = \frac{5}{1} and \frac{25}{XZ} = \frac{5}{1} \\ AB = 2\times 5 and 25 = XZ \times 5 \\ AB = 10 and XZ = \frac{25}{5} \\ AB = 10 and XZ = 5 \end{gathered}$$

 

 

We have come to the end of this class. We do hope you enjoyed the class?

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In our next class, we will continue our lesson on Geometry. We are very much eager to meet you there.

 

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