Learner Objective I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent Advanced Geometry Learner Objective I will calculate midpoints of segments and complete proofs requiring that more than one pair of tri ID: 387901
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4-1 Detour Proofs
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
Advanced GeometrySlide2
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
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Warm-Up
Given:
Prove:
STATEMENTS
REASONSSlide3
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
The Midpoint Formula
If A = and B = , then the midpoint M =
of can be found by using the midpoint formula:
A
B
MSlide4
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
Note the difference between Slope and Midpoint:
Slope is the ratio of rise to run. Thus the answer to a slope question is a ratio (fraction).
Slope is calculated using the formula:
The Midpoint is a Point. Thus the answer to a Midpoint question is an ordered pair that gives the x and y coordinates of that point.
The x coordinate of the midpoint is the AVERAGE of the x coordinates of the segment's endpoints and the y coordinate of the midpoint is the AVERAGE of the y coordinates of the segment's endpoints.Slide5
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
Example:
Find the Slope and the Midpoint of
the segment having endpoints at
(-4, 1) and (8, 7).
Slope
MidpointSlide6
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide7
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide8
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide9
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide10
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide11
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide12
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide13
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide14
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide15
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide16
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide17
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
Assignment
4.1: 1-9Slide18
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide19
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide20
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide21
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide22
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide23
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide24
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide25
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.Slide26
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide27
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide28
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide29
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide30
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide31
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide32
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide33
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide34
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide35
Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.
STATEMENTS
REASONSSlide36