3. Segment

Notes

•Segment DM and Midpoint R Segment DM has a midpoint R. Given that DM = 26 units, find the value of r if DR = r + 3 and RM = r + 3. Options: A. 8, B. 10, C. 13, D. 16 •Equation Simplification 2x = 16 = x + 8 •Right Triangle Identification Which set of lengths forms a right triangle? A. 6 cm, 8 cm, 11 cm B. 9 cm, 12 cm, 15 cm C. 5 cm, 7 cm, 9 cm D. 7 cm, 9 cm, 12 cm Correct answer: B. 9 cm, 12 cm, 15 cm •Fabric Fit Question A fabric triangle has sides of 1.5 ft, 2 ft, and 2.5 ft. Will it fit into a corner of a rectangular quilt? Yes. Calculation: 2.5 ft, 2.5 ft, and 1.25 ft (hypotenuse) suggest it fits, as the measurements satisfy the Pythagorean theorem (6.25 + 4 = 10.25, close to 6.25 + 4 = 10.25). •Proof of Segment Congruence Given: WY = XZ. Prove: WX = YZ. | Statements | Reasons | |--------------|---------| | WY = XZ | Given | | WY = XZ | Definition of congruence | | WX + XZ = WZ; WY + YZ = WZ | Segment addition | | XZ + YZ = WZ | Substitution | | WX + XZ = XZ + YZ | Transitive property | | WX = YZ | Subtraction | | WX = YZ | Definition of congruence | •Properties of Equality and Congruence - Addition, subtraction, multiplica...