"Definition Of..."
Presentation
•
Mathematics
•
9th - 12th Grade
•
Medium
+1
Standards-aligned
Brian Demcher
Used 5+ times
FREE Resource
12 Slides • 6 Questions
1
"Definition Of..."
2
Poll
Describe your comfort level with applying definitions of geometry terms.
I am very uncomfortable applying definitions of geometry.
I am somewhat comfortable after Mr. Demcher goes over the definition.
I am somewhat comfortable even before Mr. Demcher goes over the definition.
I am extremely comfortable with applying definitions of geometry.
3
"Definition of..." in Geometry
When solving proofs, we must use definitions and terms that we previously learned and convert them into an If - Then Statement.
Example: Definition of Complementary Angles. What do we know about complementary angles?
If two angles are complementary, then the two angles add up to 90 degrees.
The "If" part describes what you are given ( typically a term or a picture)
The "Then" part describes and applies the definition.
4
Complementary Angles
Apply what you know about complementary angles!
Complementary Angles equal 90 degrees when added together
If two angles are complementary, then the two angles add up to 90 degrees.
The "If" part describes what you are given (typically a term or a picture)
The "Then" part describes and applies the definition.
5
Common Terms in Proofs with Triangles
Bisects
Midpoint
Isosceles Triangles
Equilateral/Equiangular Triangles
Base Angles
Perpendicular
Right Angles
Linear Pair
Alternate Interior/Exterior Angles
Reflexive Property of Congruence
Complementary Angles
Supplementary Angles
Vertical Angles
6
2 Questions to Ask Yourself:
1. What term (most likely from the previous slide) do I recognize in there?
2. What do I know about this term from previous sections?
Example:
B is the midpoint of AC.
1. What term do you recognize from a previous section in this course?
Midpoint
2. What do I know about this term?
If something is the midpoint, then the point divides a larger segment into two smaller congruent segments.
7
B is the Midpoint of AC
If B is the midpoint of AC, then we know that the distance from A to B is the same distance from C to B so AB is congruent to BC.
8
BD bisects angle ABC
1. What term (most likely from a previous slide) do I recognize in there?
2. What do I know about this term from previous sections?
9
BD bisects angle ABC
1. What term (most likely from a previous slide) do I recognize in there?
Bisect
2. What do I know about this term from previous sections?
When an angle is bisected, the larger angle is divided into two smaller congruent angles.
10
Multiple Choice
Which picture represents the statement: B bisects Angle ABC?
11
BD bisects angle ABC
Because BS bisects angle ABC, than we know that we have the following image:
Statement: If BD bisects angle ABC, then Angle ABD is congruent to CBD.
12
Multiple Choice
Try it on your own: If Angle A and Angle B are supplementary, then....
Angle B + Angle C = 180
Angle A + Angle B = 90
Angle A + Angle B = 180
Not enough information
13
Multiple Choice
If we have ________, then we know that Angle 1 is congruent to Angle 3.
Adjacent Angles
Complementary Angles
Vertical Angles
Not enough information
14
If we have ________, then we know that Angle 1 is congruent to Angle 3.
How can we support (with a definition) that Angle 1 is congruent to Angle 3?
Are angles 1 and 3 adjacent?
Are angles 1 and 3 complementary?
Are angles 1 and 3 vertical? YES!
15
Fill in the Blanks
Type answer...
16
If Triangle ABC is an Isosceles Triangle...
Since we know that triangle ABC is an isosceles triangle, what do we know?
AB is congruent to AC (Definition of Isosceles Triangle)
Angle B is congruent to Angle C (Isosceles Triangle Theorem)
17
Multiple Choice
What can we assume from the following statement?
Triangle ABC is an equilateral triangle.
We cannot assume anything from this statement?
AB is congruent to AC.
AB is congruent to BC. BC is congruent to CA. CA is congruent to AB.
18
Triangle ABC is an equilateral triangle.
1. What term (most likely from a previous slide) do you recognize in there?
-Equilateral Triangle
2. What do I know about this term from previous sections?
-Equilateral Triangles have 3 congruent sides (as well as 3 congruent angles)
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