# Geometry Fall 2011 Lesson 48 _Using Similar triangles to prove : Geometry

### Topic

: Using proportions involving corresponding line segments

### Aim

: How can we use proportions involving corresponding line segments?

### Objectives

: 1) Students will students will know that properties of polygons that are similar.

### HW # 48

: Given: ∆𝐴𝐵𝐶 𝑚 < 𝐶 = 90 𝐷𝐸 ̅̅̅̅ Prove: 𝐴𝐷 = 𝐴𝐵 𝐷𝐸 𝐵𝐶

### Note

: Selection of definitions, theorems and postulates from this unit:

### Date

: Wednesday December 21 st , 2011 1)

A line that is parallel to one side of a triangle and intersects the other two sides in different points cuts off a triangle similar to the given triangle

. 2)

Two triangles are similar if two angles of one triangle are congruent to two corresponding angles of the other

. 3)

If a line divides two sides of a triangle proportionally, the line is parallel to the third side.

4)

If a line is parallel to one side of a triangle and intersects the other two sides, the line divides those sides proportionally

. 5)

If a line segment joins the midpoints of two sides of a triangle, the segment is parallel to the third side and its length is one half the length of the third side

. 6)

In a proportion, the product of the means is equal to the product of the extremes

. 7)

If two polygons are similar, then their corresponding angles are congruent and their corresponding sides are in proportion

.

### Do Now

: Given: ̅̅̅̅ ∥ 𝐷𝐶 Prove: 𝐴𝐸 𝐶𝐸 = 𝐵𝐸 𝐷𝐸 1

### Statements Reasons PROCEDURE

: Get students working!

Take attendance Give Back HW Write the Aim and Do Now Collect HW Go over the Do Now In the proof above, what reason could we use to prove 𝐶𝐸 𝑥 𝐵𝐸 = 𝐴𝐸 𝑥 𝐷𝐸

### Assignment #1

: Given: Parallelogram ABCD Prove: 𝐷𝐸 𝑥 𝐵𝐸 = 𝐹𝐸 𝑥 𝐶𝐸

### Statements Reasons Assignment #2

: Given: ∆𝐴𝐵𝐶 ~∆𝐷𝐸𝐹 Prove: 𝐴𝐷 𝐷𝐺 = 𝐴𝐵 𝐷𝐸

D G

### Reasons Theorem

: If two triangles are similar, the lengths of corresponding altitudes have the same ratio as the lengths of any two corresponding sides.

### Corollary

: In two similar triangles, the lengths of any two corresponding line segments have the same ratio as the lengths of any pair of corresponding sides. 2