**Using similar triangles to find slope worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on similar triangles and slope.

1. In the diagram given below, using similar triangles, prove that the slope between the points D and F is the same as the slope between the points A and C.

2. Suppose that we label two other points on line ℓ as P and Q. Would the slope between these two points be different than the slope we found in the above activity ? Explain.

3. Find the slope of the line AB using the similar triangles as a guide.

**Question 1 : **

In the diagram given below, using similar triangles, prove that the slope between the points D and F is the same as the slope between the points A and C.

**Answer :**

**Step 1 :**

Draw the rise and run for the slope between points D and F. Label the intersection as point E. Draw the rise and run for the slope between points A and C. Label the intersection as point B.

**Step 2 :**

Write expressions for the slope between D and F and between A and B.

Slope between D and F : FE / DE

Slope between A and B : CB / AB

**Step 3 :**

Extend DE and AB across our drawing. DE and AB are both horizontal lines, so they are parallel.

Line l is a transversal that intersects parallel lines.

**Step 4 :**

Because DE and AB are parallel lines and ℓ is a transversal that intersects DE and AB,

m∠FDE and m∠CAB are corresponding angles and they are congruent.

m∠FED and m∠CBA are right angles and they are congruent.

**Step 5 :**

By Angle–Angle Similarity, triangle ABE and triangle CDF are similar triangles.

**Step 6 :**

Because triangle ABE and CDF are similar, the lengths of corresponding sides of similar triangles are proportional.

FE / CB = DE / AB

**Step 7 :**

Recall that you can also write the proportion so that the ratios compare parts of the same triangle :

FE / DE = CB / AB

**Step 8 :**

The proportion we wrote in step 8 shows that the ratios we wrote in step 2 are equal. So, the slope of line ℓ is constant.

Hence, the slope between the points D and F is the same as the slope between the points A and C.

**Question 2 : **

Suppose that we label two other points on line ℓ as P and Q. Would the slope between these two points be different than the slope we found in the above activity ? Explain.

**Answer :**

No

The slope of the line is constant, so the slope between the points P and Q would be the same. Moreover, not only the two points P and Q, between any two points on ℓ, the slope would be same.

**Question 3 :**

Find the slope of the line AB using the similar triangles as a guide.

**Answer :**

**Step 1 : **

Slope is a ratio between the change in y and the change in x. That is y/x.

**Step 2 : **

Both triangles rise 2 places (y) and run 3 places (x). So the slope is 2/3.

After having gone through the stuff given above, we hope that the students would have understood "Using similar triangles to find slope worksheet".

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