This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
A polygon is a closed shape made of line segments where each line segment intersects exactly two others. The document defines different types of polygons such as triangles, quadrilaterals, pentagons, hexagons, etc. and provides characteristics of each such as the number of sides, properties of side lengths and angles, and the total sum of interior angles. Regular polygons are those with equal side lengths and interior angles, while irregular polygons do not have these properties.
This document discusses classifying and analyzing three-dimensional geometric shapes. It defines key terms like face, edge, and vertex used to describe three-dimensional shapes. Examples are provided to demonstrate classifying shapes based on these properties, identifying shapes from nets, and describing cross sections. The document also provides examples applying these concepts to cutting cheese into different shapes depending on how it is sliced. Overall, the document covers classifying, analyzing, and describing three-dimensional shapes.
Dokumen tersebut membahas tentang segiempat dan jenis-jenisnya seperti persegi panjang, persegi, jajargenjang, belah ketupat, trapesium dan layang-layang. Dijelaskan pula sifat-sifat masing-masing bangun datar tersebut seperti panjang sisi, besar sudut, dan keberadaan diagonal dan sumbu simetri. Keluarga segiempat juga digambarkan untuk membedakan jenis-jenisnya.
Garis dan sudut (faiz amri 1009069)microsoft power point 2010Faiz Amri
Dokumen tersebut membahas tentang konsep sudut dan jenis-jenisnya seperti sudut siku-siku, lancip, tumpul, lurus, dan refleks. Terdapat pembahasan mengenai hubungan antar sudut seperti sudut yang saling bertolak belakang, dalam sepihak, luar sepihak, dalam berseberangan, dan luar berseberangan.
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
A polygon is a closed shape made of line segments where each line segment intersects exactly two others. The document defines different types of polygons such as triangles, quadrilaterals, pentagons, hexagons, etc. and provides characteristics of each such as the number of sides, properties of side lengths and angles, and the total sum of interior angles. Regular polygons are those with equal side lengths and interior angles, while irregular polygons do not have these properties.
This document discusses classifying and analyzing three-dimensional geometric shapes. It defines key terms like face, edge, and vertex used to describe three-dimensional shapes. Examples are provided to demonstrate classifying shapes based on these properties, identifying shapes from nets, and describing cross sections. The document also provides examples applying these concepts to cutting cheese into different shapes depending on how it is sliced. Overall, the document covers classifying, analyzing, and describing three-dimensional shapes.
Dokumen tersebut membahas tentang segiempat dan jenis-jenisnya seperti persegi panjang, persegi, jajargenjang, belah ketupat, trapesium dan layang-layang. Dijelaskan pula sifat-sifat masing-masing bangun datar tersebut seperti panjang sisi, besar sudut, dan keberadaan diagonal dan sumbu simetri. Keluarga segiempat juga digambarkan untuk membedakan jenis-jenisnya.
Garis dan sudut (faiz amri 1009069)microsoft power point 2010Faiz Amri
Dokumen tersebut membahas tentang konsep sudut dan jenis-jenisnya seperti sudut siku-siku, lancip, tumpul, lurus, dan refleks. Terdapat pembahasan mengenai hubungan antar sudut seperti sudut yang saling bertolak belakang, dalam sepihak, luar sepihak, dalam berseberangan, dan luar berseberangan.
THIS POWERPOINT PRESENTATION ON THE TOPIC CIRCLES PROVIDES A BASIC AND INFORMATIVE LOOK OF THE TOPIC
_________________________________________________
LIKE ...COMMENT AND SHARE THIS PRESENTATION
FOLLOW FOR MORE
Module 7 triangle trigonometry super finalDods Dodong
This document provides an overview of a Grade 9 mathematics module on triangle trigonometry. It includes 5 lessons:
1. The six trigonometric ratios of sine, cosine, tangent, cosecant, secant, and cotangent and their definitions in right triangles.
2. The trigonometric ratios of specific angles like 30, 45, and 60 degrees using special right triangles.
3. Angles of elevation and depression and how they are equal in measure.
4. Word problems involving right triangles that can be solved using trigonometric functions.
5. Oblique triangles and how the Law of Sines can be used to find missing sides and angles in any triangle.
1. The document discusses different types of quadrilaterals including their definitions and properties.
2. Quadrilaterals are classified based on characteristics such as equal side lengths, parallel sides, right angles, and diagonals.
3. The main quadrilaterals discussed are rectangles, rhombus, squares, parallelograms, trapezoids, kites, and general quadrilaterals. Formulas for interior angle sums and relationships between different quadrilaterals are also provided.
Dokumen tersebut memberikan penjelasan tentang garis dan sudut, termasuk jenis-jenisnya, hubungan antara garis dan sudut, serta soal evaluasi berupa pilihan ganda mengenai materi tersebut.
The document provides information about basic geometric concepts including points, lines, planes, angles, and angle classification. It defines points, lines, and planes as undefined terms and describes their representations. The document discusses collinear and coplanar points and provides examples of naming them. It defines line segments, rays, and opposite rays and provides examples of drawing them. The document also defines acute, obtuse, right, straight, complementary and supplementary angles and discusses classifying angle measures. Follow-up activities are suggested to reinforce the concepts.
here is a ppt on geometrical figures and it gives details all about the different types of geometrical shapes and give many pictures and short definitions on them.....
it is a really good power point presentation.......
3. MATERI ESENSIAL ASPEK STATISTIKA DAN PELUANG.pptxAbdulWahid763806
Dokumen tersebut membahas tentang pelatihan matematika di tingkat MI yang mencakup aspek-aspek seperti bilangan, geometri dan pengukuran, serta statistika dan peluang. Pembahasan statistika dan peluang di MI meliputi penyajian dan interpretasi data tunggal sederhana, serta konsep rata-rata, median, dan modus data.
This document contains information about proving triangles congruent using various postulates and theorems of geometry including:
- SSS (side-side-side) postulate
- SAS (side-angle-side) postulate
- ASA (angle-side-angle) postulate
- AAS (angle-angle-side) theorem
- Hypotenuse-Leg theorem
It also defines key terms like hypotenuse and legs of a right triangle and presents the Pythagorean theorem.
Modul ini membahas tentang geometri datar khususnya segiempat. Terdapat beberapa jenis segiempat dijelaskan seperti jajargenjang, persegi panjang, belah ketupat, persegi, trapesium, layang-layang dan sembarang segiempat beserta sifat-sifat dan rumus luasnya.
This document discusses classifying and identifying different types of angles:
- It defines angles and describes four ways to name angles: using the vertex, number, or points with the vertex in the middle.
- It classifies angles as acute (<90°), right (90°), obtuse (>90°), or straight (180°) and provides examples of each.
- It explains that adjacent angles are side-by-side and share a vertex and ray, while vertical angles are opposite and congruent. Finding missing angle measures can use properties of vertical angles.
Este documento clasifica y define los diferentes tipos de ángulos. Explica que un ángulo es la intersección de dos rayos en un punto común llamado vértice. Luego clasifica los ángulos según su magnitud en nulo, convexo, llano y cóncavo. También define conceptos como bisectriz de un ángulo, ángulos complementarios, propiedades de ángulos adyacentes y opuestos por el vértice. Finalmente plantea un problema para calcular el valor de x.
The document discusses different types of shapes including 2D and 3D shapes. It defines what a shape is and provides examples of 2D shapes like circles and triangles. It also defines 3D shapes as solid objects that have length, breadth and height. Examples provided include cubes and spheres. The document also discusses properties of 2D and 3D shapes such as faces, edges and vertices. Maps are also summarized as representations of locations that use symbols, colors and scales.
THIS POWERPOINT PRESENTATION ON THE TOPIC CIRCLES PROVIDES A BASIC AND INFORMATIVE LOOK OF THE TOPIC
_________________________________________________
LIKE ...COMMENT AND SHARE THIS PRESENTATION
FOLLOW FOR MORE
Module 7 triangle trigonometry super finalDods Dodong
This document provides an overview of a Grade 9 mathematics module on triangle trigonometry. It includes 5 lessons:
1. The six trigonometric ratios of sine, cosine, tangent, cosecant, secant, and cotangent and their definitions in right triangles.
2. The trigonometric ratios of specific angles like 30, 45, and 60 degrees using special right triangles.
3. Angles of elevation and depression and how they are equal in measure.
4. Word problems involving right triangles that can be solved using trigonometric functions.
5. Oblique triangles and how the Law of Sines can be used to find missing sides and angles in any triangle.
1. The document discusses different types of quadrilaterals including their definitions and properties.
2. Quadrilaterals are classified based on characteristics such as equal side lengths, parallel sides, right angles, and diagonals.
3. The main quadrilaterals discussed are rectangles, rhombus, squares, parallelograms, trapezoids, kites, and general quadrilaterals. Formulas for interior angle sums and relationships between different quadrilaterals are also provided.
Dokumen tersebut memberikan penjelasan tentang garis dan sudut, termasuk jenis-jenisnya, hubungan antara garis dan sudut, serta soal evaluasi berupa pilihan ganda mengenai materi tersebut.
The document provides information about basic geometric concepts including points, lines, planes, angles, and angle classification. It defines points, lines, and planes as undefined terms and describes their representations. The document discusses collinear and coplanar points and provides examples of naming them. It defines line segments, rays, and opposite rays and provides examples of drawing them. The document also defines acute, obtuse, right, straight, complementary and supplementary angles and discusses classifying angle measures. Follow-up activities are suggested to reinforce the concepts.
here is a ppt on geometrical figures and it gives details all about the different types of geometrical shapes and give many pictures and short definitions on them.....
it is a really good power point presentation.......
3. MATERI ESENSIAL ASPEK STATISTIKA DAN PELUANG.pptxAbdulWahid763806
Dokumen tersebut membahas tentang pelatihan matematika di tingkat MI yang mencakup aspek-aspek seperti bilangan, geometri dan pengukuran, serta statistika dan peluang. Pembahasan statistika dan peluang di MI meliputi penyajian dan interpretasi data tunggal sederhana, serta konsep rata-rata, median, dan modus data.
This document contains information about proving triangles congruent using various postulates and theorems of geometry including:
- SSS (side-side-side) postulate
- SAS (side-angle-side) postulate
- ASA (angle-side-angle) postulate
- AAS (angle-angle-side) theorem
- Hypotenuse-Leg theorem
It also defines key terms like hypotenuse and legs of a right triangle and presents the Pythagorean theorem.
Modul ini membahas tentang geometri datar khususnya segiempat. Terdapat beberapa jenis segiempat dijelaskan seperti jajargenjang, persegi panjang, belah ketupat, persegi, trapesium, layang-layang dan sembarang segiempat beserta sifat-sifat dan rumus luasnya.
This document discusses classifying and identifying different types of angles:
- It defines angles and describes four ways to name angles: using the vertex, number, or points with the vertex in the middle.
- It classifies angles as acute (<90°), right (90°), obtuse (>90°), or straight (180°) and provides examples of each.
- It explains that adjacent angles are side-by-side and share a vertex and ray, while vertical angles are opposite and congruent. Finding missing angle measures can use properties of vertical angles.
Este documento clasifica y define los diferentes tipos de ángulos. Explica que un ángulo es la intersección de dos rayos en un punto común llamado vértice. Luego clasifica los ángulos según su magnitud en nulo, convexo, llano y cóncavo. También define conceptos como bisectriz de un ángulo, ángulos complementarios, propiedades de ángulos adyacentes y opuestos por el vértice. Finalmente plantea un problema para calcular el valor de x.
The document discusses different types of shapes including 2D and 3D shapes. It defines what a shape is and provides examples of 2D shapes like circles and triangles. It also defines 3D shapes as solid objects that have length, breadth and height. Examples provided include cubes and spheres. The document also discusses properties of 2D and 3D shapes such as faces, edges and vertices. Maps are also summarized as representations of locations that use symbols, colors and scales.
2. ÇOKGENLER
Düzlemde herhangi üçü doğrusal olmayan n tane
noktayı ikişer ikişer birleştiren doğru parçalarının
oluşturduğu kapalı şekillere çokgen denir.
Çokgenler kenar sayılarına göre isimlendirilir. Kenar
sayısı 4 olan, dörtgen; kenar sayısı 5 olan, beşgen; kenar
sayısı 6 olan, altıgendir.
3. ÇOKGENLER
Bir çokgenin içinde alınan herhangi iki noktayı birleştiren doğru
parçasının tamamı çokgenin içinde kalıyorsa çokgene dışbükey
(konveks),
doğru parçasının bir kısmı çokgenin dışında kalıyorsa içbükey
(konkav) denir.
4. ÇOKGENLER
Çokgenin iç bölgesindeki açılara,
çokgenin iç açıları, dış bölgesindeki
açılara çokgenin dış açıları denir.
Bir çokgenin ardışık olmayan iki
köşesini birleştiren doğru parçalarına
çokgenin köşegenleri denir.
[AD] doğru parçası bu çokgenin
bir köşegenidir.
5. ÇOKGENLER
Bir çokgenin n tane kenarı var ise iç açılarının
toplamı;
(n - 2) . 180°
Üçgen için ; (3 – 2) . 180° = 180°
Dörtgen için ; (4 – 2) . 180° = 360°
Beşgen için ; (5 – 2) . 180° = 540°
Bütün çokgenlerde, dış açılar toplamı 360° dır.
6. ÇOKGENLER
n kenarlı dışbükey bir çokgenin bir köşeden (n – 3) tane
köşegen çizilebilir.
n kenarlı dış bükey bir çokgenin içerisinde, bir köşeden
köşegenler çizilerek (n – 2) adet üçgen elde edilebilir.
n kenarlı bir çokgenin belirtilebilmesi için en az
(n-2)tanesinin uzunluk ve n-1 tanesinin açı olması koşulu
ile (2n-3) tane elmanın verilmesi gerekir.
7. ÇOKGENLER
Bütün kenarlarının uzunlukları ve bütün açılarının
ölçüleri eşit olan çokgenlere düzgün çokgen denir.
Düzgün çokgenin iç açılarının ölçüleri birbirine
eşittir. Düzgün çokgenin dış açılarının ölçüleri
birbirine eşittir. n kenarlı bir düzgün çokgende,
9. ÇOKGENLER
DÖRTGEN
Bir düzlemde, herhangi ucu doğrusal olmayan A, B, C,
D noktaları verilsin. [AB], [BC], [CD], [DA] doğru
parçalarının birleşim kümesine ABCD dörtgeni denir.
10. ÇOKGENLER
DÖRTGEN ÖZELLİKLERİ
1-Bir konveks dörtgenin iç açılarının ölçülerinin
toplamı ve dış açılarının ölçüleri toplamı 360°dir.
2-Kenar uzunlukları a, b, c, d olan, köşegenleri dik
olarak kesişen bir konveks dörtgenin kenarları
arasında a2
+c2
=b2
+d2
bağıntısı vardır.
12. ÇOKGENLER
YAMUK
Yalnız iki kenarı paralel olan dörtgene, yamuk denir.
Yamuğun paralel olan kenarlarına, yamuğun tabanları,
paralel olmayan kenarlarına yanal kenarlar denir.
13. ÇOKGENLER
YAMUĞUN ÖZELLİKLERİ
1-Yamuğun, yanal kenarları üzerindeki açılar bütünlerdir.
2-Yan kenarların orta noktalarını birleştiren doğru parçasına, orta taban
denir. Orta taban uzunluğu, alt ve üst tabanlarının uzunluklarının
toplamının yarısı kadardır.
22. ÇOKGENLER
EŞKENAR DÖRTGEN ÖZELLİKLERİ
Dört kenarı bir birbirine eşit olan paralelkenara eşkenar
dörtgen denir.
Eşkenar dörtgen, paralelkenarın bütün özelliklerini
taşır.
1-Köşegenler birbirlerini ortalayarak keserler.
[AC] [BD]⊥
|AK| = |KC| ve |KB| = |KD| dir.
23. ÇOKGENLER
EŞKENAR DÖRTGEN ÖZELLİKLERİ
2-Kenar uzunluğu a, köşegenleri e ve f olan eşkenar
dörtgende
e2
+ f2
= 4.a2
bağıntısı vardır.
3-Köşegenler açıortaydır ve dik olarak kesişirler.
25. ÇOKGENLER
DELTOİD ÖZELLİKLERİ
1-İkiz olmayan kenarlar arasında kalan açılar eşittir.
2-[BD] köşegeni B ile D açılarının açıortayıdır.
3-Deltoid’de köşegenler dik olarak kesişirler.
31. ÇOKGENLER
KARENİN ÖZELLİKLERİ
1-Kare, paralelkenar ve dikdörtgenin tüm özeliklerini
taşır. (Bütün kenarları eşit olduğu için eşkenar
dörtgenin de özelliklerini taşır.)
2-Köşegenler birbirlerini ortalayarak ve dik olarak
keserler.
|DK| = |KB| = |AK| = |KC| dır.
