Explore BrainMass
Share

Triangles

Diagonals of Quadrilaterals

1- prove that the diagonals of a rhombus bisect each other at right angels. 2- prove that diagonals of a kite or dart (possibly extended) intersect at right angels. (Note: kite is a convex quadrilateral in which 2 pairs of adjacent sides are congruent dart is a non convex quadrilateral in which 2 pairs of adjacent sides are

Open-Jaw Inequality

Prove the first half of the open-jaw inequality where the point G lies inside triangle DEF i.e. show that if x less than y => AC < DF. Please see the attached file for the fully formatted problems.

Right Triangles

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90° angle). How do I find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet.

Geometry Proofs : Triangles, Bisectors and Midpoints

1- Given triangle as shown (infigure 241W) with AF = 1/4 AB, AE = 1/3 and BE Intersect CF = O (BE has ray bar on top and CF has distance bar on top) prove that AO hits BC At its midpoint. 2- Use Ceva's theorem to prove that the internal bisectors of the angles of a triangle are concurrent (cevas theorem: given triangle AB

Internal bisectors and incenter of a triangle

1- Given triangle ABC, prove that an internal bisectors of an angle of a triangle divides the opposite sides (internally) into two segments proportional to the adjacent sides of the triangle. That is prove that DB/DC = AB/AC. (D is the point where e internal bisector of <A meets with BC) 2- Given triangle ABC with in-center

Triangle Word Problems : Finding Perimeter and Area

Caitlyn is a landscaper who is creating a triangular planting garden. The homeowner, Lisa, wants the garden to have two equal sides and contain an angle of 120°. Also, Lisa wants the longest side of the garden to be exactly 6 m. a)How long is the plastic edging that Caitlyn will need to surround the garden? b) What will

Geometry

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Pascal's Triangle Representation

(See attached file for full problem description) --- The question is =========== Let S_(n,0), S_(n,1), and S_(n,2) represent the sums of every third element in the nth row of Pascal's Triangle beginning on the left. For example: Row 5: 1 5 10 10 5 1 So, S_(5,0) = 1 + 10 = 11 S_(5,1) = 5 + 5 = 10 S_(5,2) =

Shortest Path Problem

1 a. Three cities are at the vertices of and equilateral triangle of unit length. Flying Executive Airlines needs to supply connecting services between these three cities. What is the minimum length of the two routes needed to supply the connecting service? 1 b. Now suppose Flying Executive Airlines adds a hub at the "cen

Geometry Application Word Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Functions and Graphs (4) Problems

(See attached file for full problem description with diagrams) --- (1) A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including ba

Area, Volume and Worker Efficiency

1. Volume of a container. A cubic shipping container had a volume of 3 cubic meters. The height was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now a3+2a2- 3a cubic meters. By how many meters were the height and width changed? 2. Worker e

Coordinate Geometry : Triangles and Lines through Triangles

The points A(-1, -2), B(7, 2) and C(k, 4), where k is a constant are the vertices of traingle ABC. Angle ABC is a right angle. 1. Calculate the value of k 2. Find the exact area of traiangle ABC 3. Find the equqtion for the stright line l passing therough B and C. Give your answer in the form of ax + by = c = 0 , where a, b

Equation of a Line Given Two Points and Area of a Triangle

A. Find an equation of a straight line passing through the points with coordinates (-1, 5) and (4, -2), giving your answer in the form ax + by + c = 0 , where a, b and c are integers. b. The line crosses the x-axis at the point A and the y-axis at the point B, and the O is the origin. Find the area of the triangle OAB.

Height and Distance: Similar triangles.

A person who is 6 foot tall walks away from a 40 foot tree towards the tip of the tree's shadow. At a distance of 10 feet from the tree the persons shadow begins to emerge beyond the tree's shadow. How much further must the person walk to completely be out of the tree's shadow?

Volume of a Tetrahedron

Find the volume of a tetrahedron with height h and base area B. Hint: B=(ab/2)sin(theta) Also, please see the attached document for the provided diagram of the tetrahedron.

Several Geometry problems

(See attached file for full problem description and diagrams) --- Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of

Fibonacci Sequence Proofs, Pascal's Triangle and Binomial Coefficients

Practice problem 1 Fn is the Fibonacci sequence (f0 = 0, f1 = 1, fn+1 = fn + fn-1). By considering examples, determine a formula for the following expressions, and then verify the formula. a. f0 + f2 + f4 + ...+f2n b. f0 - f1 + f2 - f3 + ...+(-1)n fn --------------------------------------------- Practice proble

Geometry and everyday life

Questions (also attached): A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made o