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G10 Math Q2- Week 7-Distance Formula.pptx
- 1. DISTANCE FORMULA Competency: applies the distance formula to prove some geometric properties. M10GE-IIg-2
- 2. Definition of Distance Formula The formula which is used to find the distance between two points (x1 , y1 ) and (x2 , y2 ), is called the Distance Formula. Examples of Distance Formula The distance between the points (1, 3) and (2, 5) is
- 3. REVIEW
- 5. Activity:What Figure am I ?
- 6. Distance Formula Slope Formula Midpoint Formula
- 7. Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle. slope of slope of Slope formula:
- 8. Perpendicular lines have negative reciprocal slopes. Perpendicular lines meet to form right angles. So, is a right angle is a right triangle since it contains a right angle
- 9. ANSWER KEY:
- 10. ANSWER KEY:
- 11. Using the Distance Formula in Proving Geometric Properties Many geometric properties can be proven by using a coordinate plane. A proof that uses figures on a coordinate plane to prove geometric properties is called a coordinate proof. Guidelines for placing figures on a coordinate plane. 1. Use the origin as vertex or center of a figure. 2. Place at least one side of a polygon on an axis. 3. If possible, keep the figure within the first quadrant. 4. Use coordinates that make computations simple and easy. Sometimes, using coordinates that are multiples of two
- 12. EXAMPLE: Prove that the diagonals of a rectangle are congruent using the methods of coordinate geometry. A D C B Given: ABCD with diagonals AC and BD
- 15. Activity : I MissedYou, But Now I foundYou
- 16. Activity : I MissedYou, But Now I foundYou
- 17. ASSIGNMENT: What is the Standard Form of equation of a Circle and its General Form? Read in advance page 252-262.
- 18. Content, graphics and text belong to the rightful owner. No copyright intended
Editor's Notes
- #5: a. The figures formed in #1, #2, and #3 are triangles. Each figure has three sides.The figures formed in #4, #5, #6, #7, #8, and #9 are quadrilaterals. Each figure has four sides.The figure formed in #10 is a pentagon. It has five sides. b. ABC and FUN are isosceles triangles. GOT and FUN are right triangles. c. ABC and FUN are isosceles because each has two sides congruent or with equal lengths. GOT and FUN are right triangles because each contains a right angle. d. Quadrilaterals LIKE and LOVE are squares. Quadrilaterals LIKE, DATE, LOVE and SONG are rectangles. Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms. Quadrilateral WIND is a trapezoid. e. Quadrilaterals LIKE and LOVE are squares because each has four sides congruent and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, and SONG are rectangles because each has two pairs of congruent and parallel sides and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms because each has two pairs of congruent and parallel sides and has opposite angles that are congruent. Quadrilateral WIND is a trapezoid because it has a pair of parallel sides.
- #9: a. The figures formed in #1, #2, and #3 are triangles. Each figure has three sides.The figures formed in #4, #5, #6, #7, #8, and #9 are quadrilaterals. Each figure has four sides.The figure formed in #10 is a pentagon. It has five sides. b. ABC and FUN are isosceles triangles. GOT and FUN are right triangles. c. ABC and FUN are isosceles because each has two sides congruent or with equal lengths. GOT and FUN are right triangles because each contains a right angle. d. Quadrilaterals LIKE and LOVE are squares. Quadrilaterals LIKE, DATE, LOVE and SONG are rectangles. Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms. Quadrilateral WIND is a trapezoid. e. Quadrilaterals LIKE and LOVE are squares because each has four sides congruent and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, and SONG are rectangles because each has two pairs of congruent and parallel sides and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms because each has two pairs of congruent and parallel sides and has opposite angles that are congruent. Quadrilateral WIND is a trapezoid because it has a pair of parallel sides.
- #10: a. The figures formed in #1, #2, and #3 are triangles. Each figure has three sides.The figures formed in #4, #5, #6, #7, #8, and #9 are quadrilaterals. Each figure has four sides.The figure formed in #10 is a pentagon. It has five sides. b. ABC and FUN are isosceles triangles. GOT and FUN are right triangles. c. ABC and FUN are isosceles because each has two sides congruent or with equal lengths. GOT and FUN are right triangles because each contains a right angle. d. Quadrilaterals LIKE and LOVE are squares. Quadrilaterals LIKE, DATE, LOVE and SONG are rectangles. Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms. Quadrilateral WIND is a trapezoid. e. Quadrilaterals LIKE and LOVE are squares because each has four sides congruent and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, and SONG are rectangles because each has two pairs of congruent and parallel sides and contains four right angles.Quadrilaterals LIKE, DATE, LOVE, SONG, and BEAT are parallelograms because each has two pairs of congruent and parallel sides and has opposite angles that are congruent. Quadrilateral WIND is a trapezoid because it has a pair of parallel sides.