7.5

Today in class we learned about proportional perimeters and similar triangles. We learned the Proportional Perimeters Theorem which states that if two polygons are similar then then the ratio of the perimeters is equal to the ratio of their corresponding sides. Here are the Dyknows we received in class and some examples. And also, here is the Arrow Theorem and an example.

Section 7.3: Similar Triangles

Angle-Angle Theorem (AA Thm)- If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 2 triangles are similar.

Side-Side-Side Theorem (SSS Similarity Thm)- If the lengths of the corresponding sides of 2 triangles are proportional, then the triangles are similar.

Side-Angle- Side Theorem (SAS Similarity Thm)- If an angle is congruent to another angle in a second triangle, and the length of the two sides that make up the angle are proprtional, then the 2 triangles are similar.

Similarity of Triangles

-Reflexive
-Symmetric
-Transitive

Trial

This is a posting trial!!

Section 7.2

Similar Polygons:

In order for two polygons to be similar to each other they must be one of two things:
1. Corresponding angles are congruent
2. lengths of corresponding sides are proportional

Proper Notation: When writing that two shapes are parallel always use ~

An example of two simular polygons is like the one below

These polygons are simular because their angles as shown correspond to each other. The diagram below shows that their corresponding sides are porpotional.












Another example of similar polygons is at right: the two polygons are proven similar because the ratios of corresponding sides are congruent








Vocab Review: Below are some vocabulary terms that would be helpful to know.

Section 7.1

6.2 let's see if this actually post this time

6.2 Parallelograms and such
Parallelogram- A quadrilateral with both pairs of opposite sides parallel.

Theorems:
Opposite sides of a Parallelogram are congruent
Opposite angles in a Parallelogram are congruent
Consecutive angles in a Parallelogram are supplementary
If a Parallelogram has one right angle, it has four right angles
The diagonals of a Parallelogram bisect each other
Each diagonal of a Parallelogram separates the Parallelogram into 2 congruent triangles

Section 6.6

A trapezoid is a quadrilateral with one pair of parallel lines and one pair of non parallel lines. The the sides consecutive to each of the parallel sides are called legs. If these legs are congruent that means that the trapezoid is an isosceles. Subsequently the base angles or the angles opposite the shorter parallel side are also congruent. This also works in reverse. The median of a trapezoid is created by connecting the midpoints of both the legs with a line segment. The median is parallel to the opposite bases and its distance equals the average of the two bases.

6.4

In section 6.4 we learned about rectangles.
A rectangle is a parallelogram with four right angles.
For rectangles, we learned a theorem called the Rectangle Diagonal Theorem it states that: if a parallelogram is a rectangle if and only if its diagonals are congruent.
Here is the Dyknow slide we received in class-->