Triangle Anatomy!Understanding right triangle anatomy is crucial, especially once students move into trigonometry.
Before discussing the Hypotenuse-leg Congruence Theorem, draw a blank right triangle. Have movable words of
LEG, LEG, and HYPOTENUSE. Encourage students to correctly label the right triangle by moving the terms to the
correct positions.
Pythagorean’s Theorem! This is one of the most useful theorems in mathematics; it is used for distance, finding
missing side lengths in a right triangle, and is the basis of the Law of Cosines. Use this silly memory device. You
will use Pythagorean’s Theorem enough times to causePost-traumatic Stress Disorder (PTSD).Each time you say,
“PTSD?” students should respond,[U+0080][U+009C]a^2 +b^2 =c^2 ![U+0080][U+009D]
In-class Activity!Similar to the activities showing ASA and AAS congruencies, students will use the following two
activities to show there are no such congruencies for AAA and SSA relationships.
Using Congruent Triangles
Pacing:This lesson should take one class period
Goal:The goal of this lesson to illustrate how congruent triangles can be used to determine congruent corresponding
segments or vertices and find distance.
Extension! Using the graphic organizer from theSAS and HLlesson, include the information presented in the
introduction.
Look out!This is approximately the lesson in which students will ask the question, “When will we ever need to know
why triangles are congruent? How will this apply to my life?” Encourage students to research aviation, construction,
manufacturing, and so forth to explore real world uses of triangles. Have students draft an essay with their findings
and present it to the class. Here are some real life examples: Architecture such as bridge construction and roof
rafters; proving properties of other figures, such as parallelograms, squares, rhombuses; determining congruent
sails on sailboats; ensuring stairs are the same (the risers have congruent triangles cut from them).
Arts and Crafts Time!Students confuse “drawings” with “constructions.” Stress to students that a true construction
can only be made with the following tools: compass and a straightedge. Constructions cannot be measured using
degrees from a protractor or units from a ruler. Once these two tools come into play, the construction is now
considered a drawing.
For a beginner warm up, encourage students to play with the compass. Many will make faces, animals, or flowers.
Have students decorate their drawings and post them on a bulletin board.
Take time and go through the perpendicular bisector constructions as a class.
Extension!Have students continue to practice constructions by constructing an angle bisector using the following
directions.
a. Have students draw an angle of their choice, labeling it^6 B.
b. Place the compass onBand draw an arc through both sides of the angle. Call the points of intersectionAand
C.Chapter 1. Geometry TE - Teaching Tips