Question

Dennis took the measurements of the line segments and wrote them down as shown.

Segment PA is 1.6 cm, segment PB is 2.7 cm, segment PC is 2.4 cm, and segment PD is 4.8 cm.

Describe the method you use to prove that Dennis took incorrect measurements. Use geometric theorems to write a two-column proof.

Answer 1

@ganeshie8

Answer 2

use http://www.mathopenref.com/chordsintersecting.html

Answer 3

@phi i still dont understand

Answer 4

This theorem states that A×B is always equal to C×D no matter where the chords are.

Answer 5

in your circle do you see chord AD (the line that goes from A to D) ?

notice the chord AD is split into 2 parts. AP and PD
when you multiply the length of AP times the length of PD you get a number

you should get the same number when you multiply the 2 parts of the chord BC

Answer 6

@phi I understand that i need help with the 2 column proof

Answer 7

just write
statement reason
P is the intersection of chords AB and CD Given
AP and PD are the 2 segments of chord AB whole is made up of its parts
CP and PD are the 2 segments of chord CD whole is make up of its parts
AP*PD = CP*PD Intersecting Chord Theorem

then show AP*PD does not = CP*PD so he measured wrong