Pythagorean Theorem.pptxhugyfrderawstdfyug
- 1. Grade 9 Third Quarter PYTHAGOREAN THEOREM Proves Pythagorean Theorem (M9GE–IIIi–2) 1 2 3 4 5 Lesson 9
- 2. Activate Prior Knowledge 1 Direction: Identify the indicated sides of the right triangles 1. A C B Hypotenuse: ______ Legs: ______ ______ Hypotenuse: ______ Legs: ______ ______ Hypotenuse: ______ Legs: ______ ______ h y p o t e n u s e hypotenuse hypotenuse leg leg leg leg leg leg 2. 3. ACTIVITY 1 a d H D h I E J F b e i c j f j f b a d e i h
- 3. Grade 9 Third Quarter PYTHAGOREAN THEOREM Proves Pythagorean Theorem (M9GE–IIIi–2) 1 2 3 4 5 Lesson 9
- 4. Grade 9 Third Quarter 1 2 3 4 5 Lesson 9 OBJECTIVES 1. Derives the Pythagorean Theorem 2. Find the missing parts of a right triangle using the Pythagorean Theorem : 3. Appreciate the importance of Pythagorean theorem in real life.
- 5. Acquire New Knowledge 2 Pythagorean Theorem is one of the most famous and useful mathematical principle in Plain Geometry. This theorem was named after a Greek Mathematician and philosopher Pytagoras (580- 500BC). There are at least 300 known proofs of Pythagorean Theorem. Pythagorean Theorem “ The square of the hypotenuse is equal to the sum of the squares of the legs.” 𝒄𝟐 =𝒂𝟐 +𝒃𝟐
- 6. Acquire New Knowledge 2 Given : Right with leg lengths a and b, and hypotenuse length c Prove:
- 8. Acquire New Knowledge 2 Illustrative Examples: Given with as right angle, a. If a = 3 cm, b = 4 cm, c = ______ b.If a = 7 cm, c = 25 cm, b = ______ c. If b = 3 cm, c = 4 cm, a = ______
- 9. Acquire New Knowledge 2 a. If a = 3 cm, b = 4 cm, c = ______ 3 cm 4 cm 𝑐2 =9+16 √𝑐2 =√25 𝑐=5𝑐𝑚 b. If a = 7 cm, c = 25 cm, b = ______ 7 cm 25 cm 𝑏2 =625 − 49 √𝑏2 =√576 𝑏=24 𝑐𝑚 hyp leg
- 10. Acquire New Knowledge 2 c. If b = 3 cm, c = 4 cm, a = ______ 3 cm 4 cm 𝑎2 =16 −9 √𝑎2 =√7 𝑎=√7 𝑐𝑚 leg
- 11. Application 2 ACTIVITY 2: In with find the length of the third side given the following measurements
- 12. SUMMARY 2 What is Pythagorean Theorem? “ The square of the hypotenuse is equal to the sum of the squares of the legs.” Given the right with as right angle, identify the formula and solve for the missing side. a) a = 6, b = 8, c = ? 𝑐=√𝑎 2 +𝑏 2 𝑐=√(6) 2 +(8) 2 𝑐=√36 +64 𝑐=√100 𝑐=10 b) a = 12, c = 13, b = ? b=√𝑐2 − 𝑎2 b=√(13) 2 −(12) 2 b=√169 −144 b=√25 b=5
- 13. Acquire New Knowledge 2 Application of Pythagorean theorem in real life : Some of the important real-life uses of the Pythagorean theorem are as follows: •It is the base of the trigonometric ratios that have uses in various real-life activities. •In construction, it is used to measure the number of steps needed in a staircase or to find the angle of elevation or depression of an object. •In architecture, it can be used to design shades depending on the light from the sun or the slope of the roof for the rainwater to flow easily. •In surveying where the terrain is usually uneven, the Pythagoras theorem is used to find the slope of the terrains. •For navigation, the theorem can be used to find the shortest distance.
- 14. Acquire New Knowledge 2 Application of Pythagorean theorem in real life : Some of the important real-life uses of the Pythagorean theorem are as follows:
- 15. Acquire New Knowledge 2 If the foot of a 10-meter ladder is placed 6 meters from a building, how high up the building will the ladder reach? Solution: Since the x is the leg in the right triangle 𝑥=√100 −36 𝑥=√64 𝑥=8 𝑚 The ladder reach the height of 8 meters up the building.
- 16. Assessment 4 Apply Pythagorean Theorem in solving for the missing lengths ACTIVITY 3
- 17. Additional Assessment 5 ASSIGNMENT Use the Pythagorean Theorem to find the unknown side of the given right triangle.
- 18. THANK YOU!
- 19. References 3 OTHER SUPPORTING LEARNING MATERIALS: