Learn all about the similar triangles formed in a right triangle by drawing an altitude from the right angle to the hypotenuse. Then there will be stuff about heartbeats and boomerangs.

Objective 1a

You will be able to find missing lengths in similar right triangles

In this video, I use television aspect ratios to introduce then concept of geometric mean, which we will apply to similar right triangles. Duration_7_37

Objective 1b

What happens when you draw in the third altitude to the hypotenuse of a right triangle? Let's use an index card to find out. Duration_8_18

Objective 1c

Using the results of our tastefully designed Thank You card combined with our peerless inductive reasoning skills, we formally state and apply the Right Triangle Similarity Theorem. Duration_7_40

Objective 1d

So far, we have effectively avoided discussing "Geometric Mean." Now let's see how that definition applies to similar right triangles. Duration_14_11

Objective 1e

Not every problem involving similar right triangles has a heartbeat. They may throw boomerangs instead. Duration_10_43

Objective 1f

How successful were you in measuring a heartbeat or throwing a boomerang? Let's find out. Duration_10_43

Objective 1g

Finally, we return to the idea of television screens to see how Kerns Powers developed the now standard 16:9 aspect ratio. I have a feeling it involves geometric mean. Duration_16_02

Geometry 7(A) apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

Geometry 7(B) apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.

Geometry 8(A) prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

Geometry 8(B) identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.