4.1 Detours and Midpoints Objectives: To use detours in proofs and to apply the midpoint formula.

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Presentation transcript:

4.1 Detours and Midpoints Objectives: To use detours in proofs and to apply the midpoint formula.

Procedure for Detour Proofs Determine which triangles must be congruent to reach the required conclusion. Attempt to prove that these triangles are congruent. If you don’t have enough information to prove them congruent, take a DETOUR (follow steps 3 – 5). Determine which parts are necessary in order to prove that the triangles are congruent. 4. FIND a pair of triangles (a) that you can easily prove to be congruent (b) that contain the parts needed for the main proof Prove the triangles found in Step 4 congruent 6. Use CPCTC and complete the proof

EX 1 Given: AB ≅ AD BC ≅ CD Prove: ΔABE ≅ ΔADE Statements Reasons AB ≅ AD 1. Given BC ≅ CD 2. Given AC ≅ AC 3. Reflexive ΔABC ≅ ΔADC 4. SSS BAE ≅ DAE 5. CPCTC AE ≅ AE 6. Reflexive ΔABE ≅ ΔADE 7. SAS

Theorem If A = (x1, y1) and B = (x2, y2), then the midpoint of AB can be found by using the midpoint formula

EX 2 In ΔXYZ find the coordinates of the point at which the median from X intersects YZ. A median is drawn from a vertex to the midpoint of the opposite side. Use the midpoint formula to find the coordinates of point M.

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Homework p. 173 #2 – 6 HL Practice Problems #1-4