unit 1 Day 7:

Day 7:similar triangles
Explanation:http://www.youtube.com/watch?v=ffHKcLu5Zac
Two triangles are similar if the only difference is size.

These triangles are all similar:

 

Quiz:
1)
Find whether the triangles shown are similar.

2)
Find if the pair of triangles shown is similar.

3)
ΔUVW and ΔXYZ are similar. If w = 10, z = 5, x = 4, and y = 3, find the remaining side lengths.

 key:
1)

The angles whose measure is given are not equal.
Hence, we have to compute the measures of the other angles.

In the first triangle, taking x as the measure of unknown angle, the sum of the measures of the three angles of the triangle is:


Subtracting 96 from both sides of the equation.

Similarly for the other triangle
Let the measure of two unknown angles, which are given to be equal, be y each.


Subtracting 82 from both sides of the equation


Dividing both sides of the equation by 2, we get:

As corresponding angles are not equal, the two triangles are not similar.

2) The measure of one angle is equal to 50 degrees in both triangles.

The other marked angles are not equal.
We have to compute the measure of the third angle to check if they have the same measure.

In the first triangle taking x as the measure of unknown angle the sum of three angles of the triangle is


Subtracting 120 degrees from both sides of the equation:

Similarly for the other triangle, let the measure of unknown angle be y.
The sum of the measures of the three angles is:


Subtracting 100 degrees from both sides of the equation.


Hence, the other two corresponding angles do not have the same measure.

As corresponding angles are not equal, the two triangles are not similar.

3) Writing a proportion for the lengths of corresponding sides, we get:

Using cross products, we get:


Dividing both sides by 5, we get:

Writing a proportion for the lengths of corresponding sides, we get:


Using cross products, we get:


Dividing both sides by 5, we get: