Solve each problem completely.Show your solutions and write the theorems and properties you applied to justify each step in the solution process.Illustrate each given and box your final answer. Given: Quadrilateral POST is an isosceles trapezoid with OS II PT. ER is its median.a. If OS = 3x – 2, PT = 2x + 10 and ER = 14, how long is each base?b. One base is twice the other and ER is 6 cm long. If its perimeter is 27 cm, how longis each leg?

Given quadrilateral POST is an isosceles trapezoid with OS∥PT and ER is its median.

Given: Quadrilateral POST is an isosceles trapezoid with OS I PT. ER is its median. a. If OS = 3x - 2, PT = 2x + 10 and ER = 14, how long is each base? b. One base is twice the other and ER is 6 cm long. If its perimeter is 27 cm, how long is each leg?

Given: Quadrilateral POST is an isosceles trapezoid with OS I PT. ER is its median. a. If OS = 3x - 2, PT = 2x + 10 and ER = 14, how long is each base? b. One base is twice the other and ER is 6 cm long. If its perimeter is 27 cm, how long is each leg?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.CT: Test

Problem 9CT: a Given that the polygon shown has six congruent angles, this polygon is known as an __________...

See similar textbooks

Related questions

Q: LIMA is a rhombus, If mcl = 98°, then the measure of 2M - How many triangles are formed when one…

Q: Given a trapezoid with a base of 100 m and 160 m respectively. It is divivded into two equal parts…

Q: - equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting…

A: let the length of the lots =L and breadth of the lots= x area of the lots = L×x It is given that…

Q: If C is the midpoint of AB and AB = 41 m what is the length of AC? If needed, round to the nearest…

A: Topic :- Algebra

Q: 8. If DE = 16x – 3, EF = 9x + 11, and DF = 52, find HG. E D F G

Q: If EC= 10 cm and AE = 3x- 5, for what value of x is ABCD a parallelogram? ABCD is a quadrilateral…

A: Given : ABCD is a quadrilateral with BE = ED. BD and AC are the diagonals of quadrilateral ABCD. EC…

Q: If the quadrilateral is a parallelogram, find the missing measures. Given PQ = 24, PS = 19, PR = 42,…

Q: For trapezoid RSTV, line segment RS is parallel to line segment VT, and line segment MN is the…

A: The trapezoid property are MN segment = (segment RS + segment VT )/2 MN=(38+62.6)/2 MN=50.3

Q: If a quadrilateral has EXACTLY 3 congruent sides and the 4th side is parallel to one of the other…

Q: KL. К 7х - 2 L J 12х - 22 M

A: Given: Side KL= 7x-2 Side JM= 12x-22

Q: Quadrilaterals JKLM and STUV are similar. If the length of UT = 18, then the length of KL = ___?

A: For similar Quadrilaterals :Congusative sides should be in same proportion so one's side will be…

Q: When the diagonals of rhombus MNPQ are drawn, how do the areas of the four resulting smaller…

A: Characteristics of a rhombus All sides are equal. (i) Diagonals bisect each other at right…

Q: 3. Given: Quadrilateral LIKE is a kite with LI = IK and LE = KE. a. LE is twice LI. If its perimeter…

A: Given- Quadrilateral LIKE is a kite with LI≅IK and LE≅KE. To Find- (a) The side LE, if LE is twice…

Q: The perimeter of a rhombus is 40 cm, and one diagonal is 12 cm long.How long is the other diagonal?

A: Explanation: Given a rhombus: Perimeter of Rhombus = 40cmLength of one diagonal = 12cm Formula used:…

Q: Given quadrilateral ABCD, find the values for x and y. A, Xroy+2) 112 (7x+6) B E.

A: According to given, The given quadrilateral ABCD is a rectangle because the diagonals AC=BD which…

Q: A circle has a diameter of 28 - A trapezoid has bases x and (x+2) and a height of 4.

Q: Given: Quadrilateral LIKE is a kite with LI IK and LE KE. a. LE is twice LI. If its perimeter is 21…

A: The perimeter of a kite is the sum of all sides of the kite. The area of a kite is: A=12d1d2 Where,…

Q: if ABCD is a rhombus, AC=4, and ADC is an equilateral triangle, what is the area of rhombus?

A: Drawing the figure as per the question, As we are given that AC=4 and ADC is an equilateral…

Q: If the quadrilateral below is a trapezoid, find the missing measures. (8x – 16) M 7 (61 + 20)° angle…

Q: The quadrilaterals ABCD and PQRS are similar. Find the length x of SP. B A 2.1 4.2 3.5

Q: For a quadrilateral ABCD, the measures of its angles are mZA = x + 16, mZB = 2(x + 1), mZC = ¿x -…

A: We have given measure of angles of quadrilateral ABCD . As we know According to the angle sum…

Q: The lengths of the bases of a trapezoid are 12 and 20. Find the length ofthe median

A: Given that : The lengths of the bases of a trapezoid are 12 and 20 .

Q: Which quadrilaterals MUST be parallelograms? Use the markings provided as evidence. Select yes or…

A: Given

Q: For equilateral triangle QRS shown below, (a) what is the length of one side [x] and (b) what is the…

A: Triangle

Q: Given: Quadrilateral LIKE is a kite with LI = IK and LE = KE. a. LE is twice LI. If its perimeter is…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Given quadrilateral DEFG is an isosceles trapezoid. Find DE.

Q: An new piece of support material needs to be installed in the triangular region on the house shown…

Q: Given that RSTVQ is a regular pentagon and APQR is equilateral in the figure shown, determine a) the…

Q: ABCD is a quadrilateral with BE = ED. B D. 1. Given that EC = 8.4 cm, what is the %3D E.

A: Definition: The diagonals bisect each other. One pair of opposite sides is parallel and equal in…

Q: - If George measures that one triangular plot has BC- AC = 4.9 miles, and mzC = 78°, and the other…

A: Draw the both triangles and set the relation between them.

Q: Given AE S EC , for what value of x is quadrilateral ABCD a parallelogra 4x A 3x+1 D 10 PREV 7 8 9…

Q: a. If the congruent trapezoids shown are slid together, what special quadrilateral is formed? b. Use…

A: (a) Consider the given figure: Here, CD=EF=b1AB=GH=b2Height=h……1 Also, AB∥CDEF∥GH……2

Q: 1. Given: Quadrilateral POST is an isosceles trapezoid with OS || PT. ER is its median. a. If OS =…

A: Draw the diagram and use the property of isosceles trapezoid.

Q: Given: Quadrilateral LIKE is a kite with LI IK and LE KE. a. LE is twice LI. If its perimeter is 21…

A: We have a quadrilateral LIKE in the shape of a kite. LI¯≅IK and LE¯≅KE It looks like: Part(a) We…

Q: If the area of a rhombus is 112 cm? and one of its diagonal is 14 cm find its othe

A: topic - area of rhombus from its diagonals

Q: P V R Q

Q: Two regular octagons have sides of length 6V3 and 9. The ratio of their areas is: a. 2/3:3 b. 4:3 c.…

A: We know that, all sides of a regular polygon are equal in length. If we know the length of one of…

Q: 16. Suppose that ABCD is a quadrilateral inscribed in a circle and that AC is a diameter of the…

A: We have to find measure of the angles.

Q: 1. Two consecutive sides of a parallelogram measure 3 m and 8 m, respectively. What is the perimeter…

A: "Since, you have asked multiple questions, we will solve the first questionfor you. If you want any…

Q: given the length of the medians of triangle 18.03 cm, 21.36 cm, 12.5 cm long. Determine the longest…

A: This question can be solved using the relation between length of median and length of sides of…

Q: r x. R (3x + 5)° (9x – 17)° - 'T

Q: Given: Quadrilateral POST is an isosceles trapezoid with OSI| PT, ER is its median. 3. If OS=2x-6,…

Q: The following is an isosceles trapezoid. If AP = 7.5 feet and PC = 2.3 feet, find the length of the…

Q: 1 Given: Quadrilateral POST is an isosceles trapezoid with OS || PT. ER is its median. a. If OS = 3x…

Q: For trapezoid RSTV, line segment RS is parallel to line segment VT, and line segment MN is the…

Q: 2. Given: Quadrilateral MIKE is a kite with Mi a IK and ME = KE. a. If ME is twice MI and its…

Q: olve each of the following problems. 1. A triangular parcel of land that will be used as a garden…

A: *As per the guidelines, only the first question was solved. Please repost the remaining questions…

Q: 15 If the quadrilateral is a parallelogram, find the missing measures. D. CF %3D 10 FE= %3D CE %3D E…

Q: Given: Trapezoid RSTV with RS 11 VT and MN is the median. Find the length of MN if RS = 6.5, ST =…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Solve each problem completely.Show your solutions and write the theorems and properties you applied to justify each step in the solution process.Illustrate each given and box your final answer.

Given: Quadrilateral POST is an isosceles trapezoid with OS II PT. ER is its median.
a. If OS = 3x – 2, PT = 2x + 10 and ER = 14, how long is each base?
b. One base is twice the other and ER is 6 cm long. If its perimeter is 27 cm, how long
is each leg?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

In trapezoid RSTV, RSVT and MN is the median, Find the length MN if RS=12.4 in. and VT=16.2 in. _
Circle O has a diameter of length 20cm. Chord AB has length 12cm, and chord CD has length 10cm. How much closer is AB than CD to point O?
a Given that the polygon shown has six congruent angles, this polygon is known as an __________ _________ b What is the measure of each of the congruent interior angles?
A satellite dish in the shape of a regular dodecagon 12 sides is nearly circular. Find: a mAB b mABC c mABC inscribed angle
In sphere O, the length of radius OP- is 6 in. Find the length of the chord: a QR- if QOR=90 b QS- if SOP=60
In P, whose radius has length 8in., mAB=mBC=60. Because mAC=120 chord AC is longer than either of the congruent chords AB and BC. Determine how much longer AC is than AB; that is, find the exact value and the approximate value of ACAB.
In trapezoid RSTV, RVST,mSRV=90, and M and N are midpoints of the nonparallel sides. a What type of triangle is RMN? b If ST = 13, RV = 17 and RS = 16, How long is RN? c What type of triangle is RVN? Hint: Use lengths of sides found in part b.
Given that ABCD is a square, use intuition to draw a conclusion regarding the lengths of AC- and BD-.
In isosceles trapezoid MNPQ with MNQP, diagonal MPMQ. If PQ = 13 and NP = 5, how long is diagonal MP?
In concave quadrilateral ABCD, the angle at A measures 40. ABD is isosceles, BC bisects ABD, and DC bisects ADB. What are the measures of ABC, ADC, and 1?
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._