Investigating Geometry: Proof

Henrico County Public Schools

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May 2006

Lesson 4-3: Proving Triangles Congruent (SSS, SAS, ASA)

Objective:

SOL G.6: The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

 Applet Directions 1 Close 
  1. Construct ΔDEF congruent to ΔABC.

  2. Using the circle tool tool image, construct a circle with radius AC and center at D.

  3. Using the intersection tool tool image, construct the intersection of the circle with the dotted line.

  4. Using the hide tool tool image, click on the circle that you constructed to hide it leaving the point F.

  5. This will be the point F of ΔDEF. AC = DF.
 Applet Directions 2 Close 
  1. Next, click the circle tool tool image, and construct another circle with radius AB and center at D.

  2. Construct another circle with radius BC and center at F.

  3. Use the intersection tool tool image, to construct the intersection of the two circles.

  4. Use the segment tool tool image, to construct ΔDEF.

  5. What reason can be given for why ΔABC and ΔDEF are congruent?

 Hands-On Activities Close 
  1. Triangle Proofs (PDF)
  2. Create a Triangle
  3. Explore SSS
  4. Explore SAS
  5. Explore ASA
  Other Web Sites web Close 
  1. Glencoe: On Line Quiz
 Puzzle & Problems tangram Close 

To stabilize a television antenna so that it remains perpendicular to the ground, three guy wires are attached as shown below. If the guy wires are are attached to the antenna at the same height from the ground and the measures of ∠A, ∠B, and ∠C are the same, what can you say about the length of the guy wires? Explain your reasoning.

antenna