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Related VA SOL: G.5 Time Frame: Objectives:
Materials:
Procedures: 1) Definitions a)
Geometric mean: For any two positive numbers a and b, the geometric mean of
a and b is the positive number x such that b) Corollary 1: The length of the altitude of the hypotenuse of a right triangle is the geometric mean of the lengths of the sub-segments of the hypotenuse. c) Corollary 2: The altitude of the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse. 2) Similarity in right triangles:
3) Congruence in right triangles a) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent by the Hypotenuse-Leg Theorem (HL).
b) Example to be done in groups while the teacher walks around and makes sure students are on the right path: i) Each group to put answer on board upon completion ii) Graph the points E(-1,-1), F(-2,-6), G(-4,-4), D(-6,-2) (1) Connect the points with segments iii) Find the slopes of the segments DG, GF, and GE iv)
Use the answer from above to describe
v) Use the distance formula to find the measures DE and FE vi)
Write a paragraph to prove Assessment: Assigned homework to be started in class if time permits Suggestions/Comments: This lesson would be more effective if it were to take place immediately following the lesson on proving congruency and similarity in triangles. With this prior information, the students are already familiar with techniques to prove triangles and the lesson should flow better. |
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