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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.

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

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

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

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

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

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

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

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

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

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

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

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

The Pythagorean Theorem Proof The area of the triangles is .The area of the square is (a-b)2 .So c² = 4 + (a – b) ² = 2ab + (a² - 2ab + b²) =a² + b² Theorem

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

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

Profil Group 7 : 1. Ummi Hanna Kholifah / 4101414018 2. Ainun Ni’mah / 4101414025 3. Eka Firdani Prasetyaningtyas / 4101414027 4. Novi Nur Hidayah / 4101414028

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

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

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

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

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

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