Apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles with special angle relationships. Use special right triangles to solve problems using the properties of triangles.
Number: MA.912.G.5
Title: Right Triangles
Type:
Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry
Related Benchmarks
This cluster includes the following benchmarks
| Code |
Description |
| MA.912.G.5.1: | Prove and apply the Pythagorean Theorem and its converse. |
| MA.912.G.5.2: | State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. |
| MA.912.G.5.3: | Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems. |
| MA.912.G.5.4: | Solve real-world problems involving right triangles. |
Related Access Points
This cluster includes the following access points.
Independent
| Access Point Number |
Access Point Title |
| MA.912.G.5.In.a: | Compare the length of the straight sides in a right triangle with the length of the side opposite the right angle (hypotenuse). |
| MA.912.G.5.In.b: | Identify examples of different kinds of right triangles in the environment using physical models. |
Supported
| Access Point Number |
Access Point Title |
| MA.912.G.5.Su.a: | Identify right triangles in the environment using physical models. |
| MA.912.G.5.Su.b: | Locate the right angle of right triangles and side opposite the right angle (hypotenuse) in the environment. |
Participatory
| Access Point Number |
Access Point Title |
| MA.912.G.5.Pa.a: | Identify objects, pictures, or signs with a right triangle. |
| MA.912.G.5.Pa.b: | Match objects, pictures, or signs with a right triangle by a given feature, such as length of sides. |
Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Lesson Plan
| Name |
Description |
| Rockin' Right Triangle Ratios: | Special Right Triangles and the ratios that work when you have to do to learn those ratios for 30-60-90 and 45-45-90 triangles. |
Presentation/Slideshow
| Name |
Description |
| Pythagoras' Theorem: | This resource can be used to introduce the Pythagorean Theorem to students. It provides sketches, applets, examples and easy-to-understand visual proofs as well as an algebra proof for the theorem.
It also includes interactive multiple choice practice questions on solving for a side of a right triangle, and applications involving right triangles, as well as a hands-on activity for students to do that allows them to create their own proof. |
Text Resource
| Name |
Description |
| The Pythagorean Theorem: | This overview of the Pythagorean Theorem covers its purpose, equation, application, and validity. The site also provides a number of illustrations which help students visualize the theorem, and links to related resources for further understanding. |
Video/Audio/Animations
| Name |
Description |
| MIT BLOSSOMS - The Juice Seller’s Problem: | "This video lesson
presents a real world problem that can
be solved by using the Pythagorean theorem.
The problem faces a juice seller daily.
He has equilateral barrels with equal
heights and he always tries to empty
the juice of two barrels into a third
barrel that has a volume equal to the
sum of the volumes of the two barrels.
This juice seller wants to find a simple
way to help him select the right barrel
without wasting time, and without any
calculations - since he is ignorant
of mathematics. The prerequisite for
this lesson includes knowledge of the
following: the Pythagorean theorem;
calculation of a triangle's area
knowing the angle between its two sides;
cosine rule; calculation of a circle's
area; and calculation of the areas and
volumes of solids with regular bases.
Materials necessary include: equilateral
containers of equal heights; sand; and
measuring devices. Examples of in-class
activities for the breaks between video
segments include class discussions,
individual calculations and small group
problem solving." (from MIT Blossoms' "Pythagoras and the Juice Seller") |
| Annotated Proof of the Pythagorean Theorem : | This resource gives an animated and then annotated proof of the Pythagorean Theorem. |
Virtual Manipulative
| Name |
Description |
| Right Triangle Calculator: | "Free online calculator will calculate the side lengths and angles for any . Just input any valid combination of sides and/or angles, and let the calculator do the rest! This free tool also draws a downloadable image of your triangle." (from Math Worksheets Go!) |
Student Resources
Vetted resources students can use to learn the concepts and skills in this topic.
Video/Audio/Animation
