2. ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA re- spectively and are such that AQ CP 2units. If the point R lies on AB produced |3D so that BR = lunit, prove that P, Q, R are collinear.

2. ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA re- spectively and are such that AQ CP 2units. If the point R lies on AB produced |3D so that BR = lunit, prove that P, Q, R are collinear.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 40E: Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible,...

See similar textbooks

Related questions

Q: In the figure, QN¯¯¯¯¯¯¯¯ is the perpendicular bisector of LM¯¯¯¯¯¯¯¯¯.Which of the following can be…

A: Introduction: Congruency is a very significant property of a triangle. Two triangles are referred to…

Q: In the image shown, which points are collinear with point P? Y X' X P Z' 02018 Gynlyon, Inc. Points…

A: we will use basic definition of Co- linear points

Q: What theorem can be used to prove these triangles are congruent? 16 16 13 13 A. SAS В. HL C. neither

A: Topic = Triangle Correct answer = SAS

Q: 11. Suppose ADEF = AWXY. Which choice below shows corresponding parts to congruent triangles that…

A: We have, △DEF≅△WXY

Q: 6. The median to the base of an isosceles triangle is the perpendicular bisector of the base.…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. sement Iheason Prove: AADE…

A: Given a parallelogram ABCD with diagonals AC and BD intersecting at E.

Q: What theorem can be used to prove these triangles are congruent? A. SAS В. HL C. neither

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. Prove: AADE ACBE "AE CE…

A: topic - congruence of triangles

Q: Drag the postulate or theorenm that proves the triangles are congruent. b AOKR AAHR a. ATSU AXVW…

Q: 15. What theorem would be used to prove the triangles below congruent? V W Y. z- SSS SAS AAA SSA

A: Side angle side (SAS) If two sides and the included angle of one triangle are equal to two sides…

Q: In the diagram below of ADAE and ABCE, AB and CD intersect at E, such that AE = CE and ZBCE = ZDAE.…

A: We have, In triangles △DAE and △BCE AE=CE∠DAE=∠BCE

Q: M 2) A KLJ = A MLN

A: Given data: In ∆KLJ and ∆MLN The length of the side JK=NM. ∠KJL=∠MNL

Q: Use Theorem 5.6.1 and the drawing R to complete the proof of this theorem: "If a line is parallel to…

A: Basic proportionality theorem states that a line parallel to one side of a triangle intersects the…

Q: 4. Given AM CM and BM DM Prove ABCD is a parallelogram. A B (Prove each opposite sides are congruent…

Q: 2. Suppose that APOR is isosceles with side PQ congruent to side PR as shown in the figure below.…

Q: 11 Prove the following triangle is an isosceles triangle. Given: OL OY, LY E 3, and ZL is 3. 4…

Q: AB is perpendicular to AD CB is perpendicular to CD DA is congruent to DC Prove: Triangle ABD is…

A: 1. Statement: AB¯⊥AD¯, CB¯⊥CD¯, DA¯≅DC¯ Reason: Given data of the problem. 2. Statement: ∠A and ∠C…

Q: 9. If you know that Point M is the midpoint of TS and UR, which of the triangle congruence methods…

A: The solution is :

Q: If any Point o inside eR ouside a tetrahedron ABCD is Joined to the Vertices and AO BO, Co ,DO are…

Q: 24. Which pair of triangles cannot be proven congruent using the HL theorem? T O K M

Q: 4)Prove that the triangles are similar. 12 A 12 18 FAABC~ADEF by SSS~ -AABC~AEDF by SSS~ -AABC~AFED…

Q: 2. Suppose that T, U, and V are the points where the incircle of AABC touches the sides BC, AC, and…

A: 2) Formula Used : Ceva's Theorem : For any ∆ABC AT , BU and CV intersect at a point O, if ATVB…

Q: Which two triangles are congruent by the SAS Theorem? Complete the congruend statement. R RST E DBC…

A: We have to check

Q: Consider the incomplete paragraph proof shown. Given: Isosceles AABC with AB BC. Prove: LA LC A D C…

A: Here we have to proof ∠A≅∠C

Q: elow. 7 Z

Q: Given the following information about two triangles, A CAT and A DOG : ZC 설 ZD CA DO AT 스 OG CT - DG…

Q: where ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such…

A: Given: AB = AC <ABP = <ACP

Q: 1. Let AABC be an equilateral triangle, where the vertices are labeled in counter clockwise order.…

Q: What theorem can be used to prove these triangles are congruent? 12 6. 12 6. A. SAS B. HL C. neither

A: We know the HL theorem ....."if the hypotenuse and leg of one right triangle are congruent to the…

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. sement Prove: AADE ACBE…

A: Given: As per the instruction, we will be proving ∆ADE≅∆CBE. We have that the parallelogram ABCD…

Q: 1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in…

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: In the sketch O is the centre of the circle and C and D are angies in segment AB of the circle (or.…

A: Given Circle with center O. And ∠C and ∠D are anɡles subtended by same chord AB To prove that ∠C =…

Q: 12. What information is needed to prove that CD is a perpendicular bisector for KM K L M D

A: We need to prove CD is a perpendicular bisector for KM. if CD is a perpendicular bisector for KM,…

Q: 1. Write a coordinate proof to prove the diagonals of an isosceles trapezoid are congruent. Gien…

Q: 8. to 12 3. 4. 7. agram above gles would be congruent under the vertical rem?

Q: 2. If quadrilateral JKLM is inscribed in a circle and 2J and ZK are sup- plementary angles, then LJ:…

A: Given that, Quadrilateral JKLM is inscribed in a circle. ∠J and ∠K are Supplementary Angles. Hence,…

Q: B E D Which pair of triangles can be established to be congruent to prove that 2DAB = ¿BCD?

A: Two triangle are said to be similar by side Angle side method

Q: Given:XW=XY Statement Reason WZ=YZ Prove: AXWZ -ΔΥΥΖ w Y

A: (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another…

Q: Polnts C, D, and E are collinear on CE, and CD: DE =. C Is %3D located at (1, 8), D is located at…

Q: In ARAE and ATAE, ZRAE is adjacent to 2TAE. RA AT and RE ET. Prove that the two triangles are…

A: We will use the criteria for congruence of triangles.

Q: ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA re- spectively and are…

Q: 1. What information would you need to prove the triangles below are congruent using the HL theorem?…

Q: In the given figure, PQRS is a quadrilateral in which A, C, B and D are the mid-points of PQ, QR, RS…

A: In the given figure, we connect A to C, A to D, B to C and B to D. Also draw a diagonal SQ

Q: 1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in…

A: Topic = Geometry As per guidelines , At a time only one question can be answered. please repost for…

Q: c. If RO = 3x – 12 and RC = 2(x – 2), find x and RO. 2. In Figure 4, OL = IL and mlIPL = M20TL. a.…

Q: What theorem can be used to prove these triangles are congruent? 6. 9. A. SAS B. HL C. neither 5

A: In the SAS rule two triangle are congruent if they are same in two side and one angle. But in given…

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. Prove: AADE ACBE sement…

A: In given figure For ∆ADE &∆BEC 1) AD= BC ( opposite sides are parallelogram are equal and…

Q: Let ABC be a triangle with orthocenter H, incenter I and circumcenter O. Prove that: (a) If ∠A is…

A: Proceed as shown

Q: 11. Which of the following would NOT be needed to prove that the triangles are congruent? Given:…

Question

2. ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA re-
spectively and are such that AQ CP = 2units. If the point R lies on AB produced
so that BR = lunit, prove that P, Q, R are collinear.

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

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 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._
Given: Equiangular RST Prove: RV bisects SRT RVS is a right
Consider regular pentagon RSTVQ not shown. Given that diagonals QT and VR intersect at point F, show that VFFR=TFFQ.
Does it follow from Exercise 30 that ADE is also congruent to CBE? What can you conclude regarding AE and CE in the drawing? What can you conclude regarding DEandBE?
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2
Refer to the prisms of Exercises 1 and 2. Which of these have symmetry with respect to a point?
Given: Regular pentagon ABCDE with diagonals BE and BD. Prove: BEBD HINT: First prove ABECBD.
The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent AB? HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Each side of square RSTV has length 8. Point W lies on VR- and point Y lies on TS- in such a way to form parallelogram VWSY, which has an area of 16units2. Find the length of VW-.
Consider XYZ triangles not shown a Which side is included by X and Y?_ b Which angle is included by sides XY and YZ?_