GEOMETRY GROUP 7 Loading... TRIANGLE Classifying Triangles The Pythagorean Theorem Special MATERI Classifying Triangles TRIANGLE The Pythagorean.

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4 GEOMETRY GROUP 7 Loading...

5 TRIANGLE Classifying Triangles The Pythagorean Theorem Special
MATERI Classifying Triangles TRIANGLE The Pythagorean Theorem Special Triangles Silakan Anda ganti judul utama, kelas dan semesternya dengan cara mengklik dua kali pada objek yang akan dirubah. Sesuaikan juga jumlah dan nama menu utama pada materi pembelajaran anda. Jika lebih cukup anda delete dan jika kurang anda bisa copy-paste. Tombol-tombol kurikulum, evaluasi, profil, referensi, bantuan, speaker, dan silang exit hanya bisa diedit di dalam slide master. Caranya klik View > Master > Master Slide.

6 We can classify triangles according to
Classifying Triangles Based on the sides We can classify triangles according to the lengths of the sides or by the measure of the angles Based on the angles

7 Equilateral Triangle An equilateral triangle is a triangle with three
Based on the sides Equilateral Triangle An equilateral triangle is a triangle with three congruent sides Equilateral Isosceles scalenes

8 If a triangel is isosceles, then its base angles are congruent
Based on the sides Isosceles Triangle An isosceles triangle is a triangle with at least two congruent sides Equilateral If a triangel is isosceles, then its base angles are congruent Theorem Isosceles scalenes Proof

9 Proof Based on the sides PROOF
Given : Let ∆ABC be isosceles with CA CB Prove : Plan : Let D be the midpoint of AB. Draw CD and prove that ∆CAD ∆CBD Equilateral Isosceles scalenes

10 Proof Based on the sides Statements Reasons Equilateral Isosceles
1. ∆ABC is isosceles with CA CB 1. Given 2. D is the midpoint of AB 2. Every line segment has one and only one midpoint. 3. ∆CAD ∆CBD 3. A segment from the vertex angle to the midpoint of the opposite side forms a pair of congruent triangles (Theorem 4 – 2) 4. 4. CPCTC Equilateral Isosceles scalenes

11 Scalene Triangle A scalene triangle is a triangle with no congruent
Based on the sides Scalene Triangle A scalene triangle is a triangle with no congruent sides Equilateral Isosceles scalenes

12 Acute Triangle An acute triangle is a triangle with three acute angles
Based on the angles An acute triangle is a triangle with three acute angles Acute Right Obtuse Equiangular

13 Right Triangle A right triangle is a triangle with a right angle
Based on the angles A right triangle is a triangle with a right angle Acute Right Obtuse Equiangular

14 Obtuse Triangle An obtuse triangle is a triangle with an obtuse angle
Based on the angles An obtuse triangle is a triangle with an obtuse angle Acute Right Obtuse Equiangular

15 Equiangular Triangle An equiangular triangle is a triangle with three
Based on the angles An equiangular triangle is a triangle with three congruent angles Acute Right Obtuse Equiangular

16 The Pythagorean Theorem
If ∆ABC is a right triangle, then the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs Theorem Proof

17 The Pythagorean Theorem
Proof Given: Right triangle ABC with hypotenuse length c and leg lengths a and b Prove : c2 =a2+b2 Analysis : Build upon ∆ABC like those shown in example 1-3. The square upon a has area a2. The square upon side b has area b2. The square upon c has area c2. The square upon side c consists of four triangles to ∆ABC and a square.The figure shows that the length of the side of the small square is a-b.We can find the area of the large square by adding the areas of the four triangles to the area of the small square. Theorem

18 The Pythagorean Theorem
Proof The area of the triangles is The area of the square is (a-b)2 .So c² = (a – b) ² = 2ab + (a² - 2ab + b²) =a² + b² Theorem

19 Pembuktian Cara Yang Lain
The Pythagorean Theorem Gambar tersebut adalah gambar sebuah trapesium yang dibentuk dari 3 segitiga. Luas trapesium tersebut adalah  . dicari menggunakan rumus luas trapesium. Yaitu setengah dikalikan dengan jumlah sisi yang sejajar dikali tinggitrapesium. Mencari luas bangun datar diatas dapat juga menggunakan jumlah luas segitiga (perhatikan gambar). Yaitu     . Theorem

20 Pembuktian Cara Yang Lain
The Pythagorean Theorem Pembuktian Cara Yang Lain Luas yang dihitung adalah Luas Trapesium dan Luas Segitiga, sehingga diperoleh, Theorem

21 Profil Group 7 : 1. Ummi Hanna Kholifah / 4101414018
2. Ainun Ni’mah / 3. Eka Firdani Prasetyaningtyas / 4. Novi Nur Hidayah /

22 Geometry With Aplication and Problem Solving
Referensi Geometry With Aplication and Problem Solving

23 Theorem 1 Proof The length of the hypotenuse of a 45°-45°-90°
Special Triangels The length of the hypotenuse of a 45°-45°-90° triangle is times the length of a leg Theorem 1 Theorem 2 Proof

24 Theorem 1 PROOF A C B Special Triangels Theorem 1 45° Theorem 2 x 45°

25 Theorem 2 Proof The length of the longer leg of a 30°-60°-90°
Special Triangels The length of the longer leg of a 30°-60°-90° triangle is times the length of the hypotenuse or times the length of the shorter side Theorem 1 Theorem 2 Proof

26 Theorem 1 PROOF A x B D C Special Triangels Theorem 1 Theorem 2 30°
60° B D C

27 THANK YOU GROUP 7 Rombel 2