1lvonnalli No Space Heading 1 Paragraph Style DIRECTIONS Use

1.lvonnalli No Space. Heading 1 Paragraph Style DIRECTIONS: Use the Reason for Proofs Document to complete the two-column proof. There are two Parts. Part A is required and Part B is Bonus! Part A (10 points) GIVEN: J is the midpoint of FHand GH I FI PROVE: 1] Statement Reason I.) is the midpoint of FR 2. GH IFI 1. Given 2. Given 3. 4. Alternate Interior Angle Theorem 5. 6 7. 6. 7, G)

Solution

5) Corresponding angle theorem .GF and IF are parallel.GI is the transversal.Hence angle G=angle I

7) In triangle GHJ and IJF ,angle GJH and angle IJF are equal(opposite anlges) .Hence all three angle are equal. Further , FJ=JF(Since J is the midpoint of HF.). Hence both triangles are congruent. Hence GJ=IJ.

3) FJ=JH due to corresponding sides of congruent triangle.