"Definition Of..."

"Definition Of..."

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.

​"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.

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​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.

​Complementary Angles

Apply what you know about complementary angles!

1. ​Complementary Angles equal 90 degrees when added together

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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.

​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

​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?

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​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.

​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.

​BD bisects angle ABC

​1. What term (most likely from a previous slide) do I recognize in there?

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​2. What do I know about this term from previous sections?

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​​BD bisects angle ABC

​1. What term (most likely from a previous slide) do I recognize in there?

• ​Bisect

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​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.

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Multiple Choice

Which picture represents the statement: B bisects Angle ABC?

​BD bisects angle ABC

Because BS bisects angle ABC, than we know that we have the following image:

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Statement: If BD bisects angle ABC, then Angle ABD is congruent to CBD.

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

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

​If we have ________, then we know that Angle 1 is congruent to Angle 3.

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​How can we support (with a definition) that Angle 1 is congruent to Angle 3?

1. ​Are angles 1 and 3 adjacent?

2. ​Are angles 1 and 3 complementary?

3. ​Are angles 1 and 3 vertical? YES!

Fill in the Blanks

​If Triangle ABC is an Isosceles Triangle...

​Since we know that triangle ABC is an isosceles triangle, what do we know?

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1. ​AB is congruent to AC (Definition of Isosceles Triangle)

2. Angle B is congruent to Angle C (Isosceles Triangle Theorem)​

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.

​Triangle ABC is an equilateral triangle.

​1. What term (most likely from a previous slide) do you recognize in there?

​-Equilateral Triangle

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​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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