1. What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each. 2. We can use the Pythagorean Theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of t
1) In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant. 2) The chemical retardants are freight shipped from
1) Solve the following equations. a) sqrt(x) - 1 = 4 b) sqrt(x^3) = 8 c) third root of x^2 = 4 2) Is sqrt(x^2) an identity (true for all values of x)? Answer: Explain your answer in this space. 3) For the equation x - sqrt(x) = 0, perform the following: a) Solve for all values of x that satisfies the equatio
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
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
Geometry Proofs : Triangles and Internal and External Bisectors; Length of Altitude ( Height) and Isoceles Triangles
1- If we have a triangle ABC, then prove that the internal and external bisectors of the angle of a triangle are perpendicular (assume for angle A) 2- Prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles.
(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) =
See attached pdf file for problem and diagram regarding angles.
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 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
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
An equilateral triangle is inscribed in a circle of radius 100. The area of the circle which lies outside of the triangle is shaded. The process continues to infinity. What is the radius for the second area/ third area/ fourth area? Side of first area/ side of second area/ side of third area/ side of fourth area? Area
Find the sum of the measures of the five acute angles that maup up this star...... OK so for this I noticed the 5 triangles that make up the star so i multiplied 180 x 5=900 Then to get the acute angles I did 180/5 and got 36... So the triangle measure would be 72 + 72 +36=180 Acute angles = 36....??? Second problem..
1. The measures of the angles of a triangle are in the ratio of 2:3:4. What is the measure of the smallest angle? 2. Each side of a rhombus measures 10 inches. If one diagonal of the rhombus is 12 inches long, what is the length of the other diagonal?
The diagram below (see attachment) shows a triangle ABC whose vertices are at A (-1, 3), B (6, 5) and C (8, -3). The line BP is perpendicular to the line AC, and M is the midpoint of BC. Note that BP is called an altitude of triangle ABC and that AM is called a median of triangle ABC. a) Find the gradient of i) The
(a) Figure 1 shows a closed area ABCDEF in which ABDE is a rectangle and BCD and AFE are equilateral triangles. AE x cm and AB y cm. (i) Find, in terms of x andy, a formula for the area enclosed by the figure ABCDEF and a formula for the perimeter ABCDEF. (ii) Find the minimum perimeter (to two decimal places) of ABCDEF enclos
Please give answer and explanation and or steps if needed please to check my work. 1) Draw a right triangle whose sides (not the hypotenuse) have lengths of 8 and 15. Angle A is adjacent to the side of 8, and angle B is adjacent to the side with the length of 15. The tan A=? 2) For the same triangle in question 1 do f
Step 1. Draw an acute scalene triangle. Label the vertices A, B,C on the interior of each angle. Step 2. Construct a segment congruent to line segment AC. Label the endpoints D and E. Step3. Adjust the compass setting to the length of line segment AB. Place the compass at point D and draw a large arc above line segment D
If A,B,C are noncollinear in a metric geometry prove that triangle ABC is convex.
The perimeter of a building is 74'by 59'by 103'by 121'. How can the square footage of the building be calculated?
Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.
Determine whether or not the argument below is valid. Transcribe it into symbolic notation and if it is valid, provide a derivation of the conclusion from the premises using only primitive rules of inference. The area of a triangle is the area of a three sided figure. Since triangles are three sided.
Prove that in a metric space, if C lies between A and B and O is any other point, then OC<=OA + OB. (Hint make 3 applications of the triangle inequality) Triangle inequality: For triangle ABC AB+BC=>AC
In this question ABC and PQR are two triangles, and the lengths of the sides opposite the angles A,B,C P, Q, R are a,b,c,p,q,r, respectively. Choose the THREE false statements. Options. A. If angle A= angle Q and angle B= angle P. then it must follow that c b --- = -- r p B. I
Suppose that the triangle ABC has three edges a=BC=4sqrt(3) , b=AC=4 and c=AB=4. Find angle ABC and BAC.
The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry. The perpendicular bisectors of the sides of a triangle meet in a point O that is the center of the circumscribed circle. a) According to a theorem from geometry, the measure of the angle
In triangle ABC, the lengths of line AB and line BC equal 13 centimeters. If the perimeter of triangle ABC is 36 centimeters, what is the area in square centimeters of triangle ABC?
A 1 acre field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each of the side of the post on the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is the total area the two sheep have to themselves?
A triangle with a 90 degree angle has sides of 39, 15, b. Solve for b.
Construct a right angled triangle such that the altitude to the hypotenuse and the median to the hypotenuse have lengths r and s respectively.