Question Video: Applying Properties of Similarity | Nagwa Question Video: Applying Properties of Similarity | Nagwa

# Question Video: Applying Properties of Similarity

The figure shows two triangles ๐ด๐ต๐ถ and ๐ท๐ธ๐น. Work out the measure of angle ๐ด๐ถ๐ต. Work out the measure of angle ๐ท๐ธ๐น. What do you notice about the measures of the angles in both shapes? Are the two triangles similar?

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### Video Transcript

The figure shows two triangles ๐ด๐ต๐ถ and ๐ท๐ธ๐น. Work out the measure of angle ๐ด๐ถ๐ต. Work out the measure of angle ๐ท๐ธ๐น. What do you notice about the measures of the angles in both shapes? Are the two triangles similar?

In the diagram, weโre given the two triangles. In each triangle, weโre given two of the angle measurements, and we need to find out the missing angle. Letโs begin with our first question to find the measure of angle ๐ด๐ถ๐ต. In order to answer this, we can remember that the angles in a triangle add up to 180 degrees. We can therefore work out 180 degrees subtract 71.6 degrees subtract 63.4 degrees, which gives us 45 degrees. So our answer to the first question is that angle ๐ด๐ถ๐ต is 45 degrees.

In the second question, we need to find the angle ๐ท๐ธ๐น in triangle ๐ท๐ธ๐น. So weโll use the fact that the angles in a triangle add up to 180 degrees. This time weโre working out 180 degrees subtract 63.4 degrees subtract 45 degrees. This gives us 71.6 degrees. And so this is our answer for the measurement of angle ๐ท๐ธ๐น.

In the third part of the question, weโre asked what we notice about the measurement of the angles in both shapes. If we look at each triangle individually, we donโt have any equal angles or even two angles equal which would say that itโs an isosceles triangle. So letโs look at both of the shapes.

Weโve got two angles that are 45 degrees, angle ๐ด๐ถ๐ต and angle ๐ท๐น๐ธ. The angle at ๐ด and the angle at ๐ธ are both 71.6 degrees, and we also have another pair of equal angles. Angle ๐ต and ๐ท are both given as 63.4 degrees. We could then answer this question by saying that these angles are equal. We donโt mean that all the angles are exactly the same, but we mean that corresponding pairs of angles are equal.

This fact will help us to answer the fourth question. Are the two triangles similar? We can recall that two triangles would be similar if the corresponding pairs of angles are equal and the corresponding pairs of sides are in proportion. We can in fact prove that two triangles are similar by using the AA rule. That means we show that we have two pairs of corresponding angles equal. We have already demonstrated that we have, in fact, got three pairs of corresponding angles equal. So we can answer this question by saying yes; triangles ๐ด๐ต๐ถ and ๐ท๐ธ๐น are similar.

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