Back to: MATHEMATICS JSS3

**Welcome to Class !!**

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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.

- If two angle of one triangle is equal to two angles of the other.
- If two pairs of sides are in the same ration and their included angles are the same.
- 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)

= 110^{0 }

Similarly, in ∆XYZ

<Z = 180^{0} – (110^{0} + 32^{0})

= 38^{0}

<A = <x = 110^{0} , < B = <Y = 32^{0} and

<c = <z = 38^{0}

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:

$\frac{AB}{2}=\frac{25}{XZ}=\frac{35}{7}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Hence:\frac{AB}{2}=\frac{35}{7}and\frac{25}{XZ}=\frac{35}{7}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{AB}{2}=\frac{35}{7}and\frac{25}{XZ}=\frac{35}{7}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{AB}{2}=\frac{5}{1}and\frac{25}{XZ}=\frac{5}{1}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}AB=2\times 5and25=XZ\times 5\phantom{\rule{0ex}{0ex}}AB=10andXZ=\frac{25}{5}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}AB=10andXZ=5$

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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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