# Geometry | Mathematics problem solving skills

Geometry is an essential branch of mathematics, which makes it important for any student to have a detailed, well-rounded knowledge of trigonometry that covers a variety of topics. Geometry is the fourth math course in high school and will guide you through among other things points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles and area. This Geometry math course is divided into 10 chapters and each chapter is divided into several lessons. Under each lesson you will find theory, examples and video lessons. Talent Academy hopes that you will enjoy studying Geometry online with us!

Sample of some problem with their solution from this courses.

Pro :- Two angles of a triangle measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures 6√ 2 units, what is the sum of the lengths of the two remaining sides?
Sol ;- Given that two angles of a triangle measure 30 and 45 degrees with side of the triangle opposite the 30-degree angle measures 6√ 2 units,  draw  a perpendicular line from point B to point D which creates a two right angle triangles. Consider  right angle triangle  BCD ,  whose angles at D and B is 90 and 45 respectively.  let angle at C be "S", the sum of  angles of  a triangle is 180, therefore the sum of triangles in triangle BCD is, S+ 45 + 90 =180; S= 45.  Triangle BCD is a isosceles right angle triangle, the hypogenous is given as BC =  6$\sqrt{2}$, let  CD and DB be  length "X" respectively, using Pythagoras theorem  we get ,  CD^2 + BD^2 =  BC^2; X^2 +X^2 = (6$\sqrt{2}$)^2; we get X = 6.  Now consider right angle triangle  ADC ,  whose angles at D and A is 90 and 30 respectively.  let angle at C be "Z", the sum of  angles of  a triangle is 180, therefore the sum of triangles in triangle ADC is, Z + 30 + 90 =180; Z = 60.  Triangle ADC is a right angle triangle, from the previous step we know that length of  CD is  6 , extend CD and A  till they meet at point  P of angle 60, we a equilateral triangle. We see CD + DP = CP = 12, therefore sides of CA and AP  are length of 12. Let  AD be Q , using Pythagoras theorem in triangle ADC  we get ,  CD^2 + Q^2 =  AC^2; 6^2 +Q^2 = (12)^2; we get Q = 6$\sqrt{3}$, therefore the sum of the sides of the triangle ABC is,  AB + BC + CA = 18+6*√ 3

Que :- A cylindrical jar with height 8 inches and diameter 6 inches is filled to 75% of its capacity with juice. The juice is then poured into another cylindrical container with a 10 inch diameter and height of 4 inches. To what percent of its capacity is the second jar filled with juice? (Mathcouns Competitions).
Ans ;54 (percent)

From architecture to engineering, trigonometry is widely used in several common careers. Gaining an understanding of trigonometry opens a wide range of doors in the field of mathematics for students interested in continuing their study.

Talent academy makes sure to cover all concepts and has divided the courses based on students interest, students can enroll to the necessary schedule.

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Angles and triangles

• Angles and triangles
• New Angles and triangles

Classification of Triangles

• Classification of Triangles

Similar Triangles

• Similar Triangles

Pythagoren Thoerem

• Pythagoren Thoerem

Trapezoids

• Trapezoids

Parallelogram

• Parallelogram

Angle Bisectors and Medians

• Angle Bisectors and Medians

Triangular Inequality

• Triangular Inequality

Area Method

• Area Method

Polygons

• Polygons

Clock Angles

• Clock Angles

Circles

• Circles

Coordinate System

• Coordinate System

Lines and Equations

• Lines and Equations

Volume

• Volume

Angle Basics

• Angle Basics

Angles in a Polygons

• Angles in a Polygons

Length and Perimeter

• Length and Perimeter

Area

• Area

Special Right Triangles

• Special Right Triangles

Mini Geometry: Circles and triangles

• Right Triangles
• Circles and Right Triangles
• Circles and Triangles Revisited
• More Circles and Right Triangles
• Circles and Area Revisited
• Geometry/Auxiliary Lines & Special Right Triangles
• Geometry/30-60-90 Right Triangles
• More 30-60-90 Right Triangles
• Labeling Figures: A Geometry Problem Solving Strategy
• Trapezoids and Triangles

Mini Analytic Geometry

• Analytic Geometry
• More Analytic Geometry
• Even more Analytic Geometry

Mini Geometry: Area and Volume

• Area and Volume
• Relationships Between a Box's Dimensions, Volume and Surface Area
• Area of Irregular Polygons Reboot
• Areas of Irregular Convex Polygons
• Composed and Decomposed Area and Volume
• Maximum Area of Inscribed Rectangles & Triangles

Mini Geometry: Similar triangles

• Similar Triangles
• Tangent Segments & Similar Triangles
• Similar Triangles and Proportional Reasoning
• Similarity and Proportional Reasoning
• Using Similarity to Solve Geometry Problems

Mini Geometry: Three Dimensional Figures

• 3-D Geometry
• Three-Dimensional Figures

Angle Chasing

• Angle Chasing

Circles

• Circles

Counting

• Counting

Functional Equations

• Functional Equations

Functions and Representations

• Functions and Representations

Mass Point

• Mass Point

Mathematical Principles

• Mathematical Principles

Modular Arithmetic

• Modular Arithmetic

Number Sense

• Number Sense

Polynomials

• Polynomials

Probability and Statistics

• Probability and Statistics

Sequences and Series

• Sequences and Series

Three-Dimensional Geometry

• Three-Dimensional Geometry

Triangles and Polygons

• Triangles and Polygons

Word Problems

• Word Problems