Transcript POWERPOINT JEOPARDY - Mrs. Robinson's Webpage

Chapter 1
Conditional
Statements
Constructions
Proofs,
Props, Posts.
Proofs
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QUESTION:
Complementary angles sum to what
measure?
ANSWER:
•90°
QUESTION:
Sketch & label:
Points F, R, and G are collinear and R is
the midpoint of 𝐹𝐺.
ANSWER:
QUESTION:
•∠𝐷𝐸𝐹 and ∠𝐹𝐸𝐺 are supplementary. If
m∠𝐷𝐸𝐹 = 9𝑥 + 1 and m∠𝐹𝐸𝐺 = 8𝑥 + 9,
classify ∠𝐷𝐸𝐹?
(hint: finding the measure first would be a good
start…)
ANSWER:
•∠𝐷𝐸𝐹 is obtuse
QUESTION:
H bisects 𝑊𝑌. If 𝑊𝑌 = 4𝑥 − 6 and 𝐻𝑌 = 5,
what is the value of 𝑥?
ANSWER:
•𝑥 = 5
QUESTION:
An angle is ten less than four times its
complement. What are the measures of the
angles?
ANSWER:
•20°, 70°
QUESTION:
Write the statement below as a conditional
statement:
Jack will fall if he fetches the water.
ANSWER:
If Jack fetches the water, then he will fall.
QUESTION:
Identify the hypothesis & conclusion in the
statement:
Goldie will win the tournament if she beats Joy.
ANSWER:
Hypothesis: Goldie beats Joy
Conclusion: Goldie will win the tournament
QUESTION:
Consider the statement:
If it is Sunday, then Chloe visits her grandma.
It is Sunday.
Make a conjecture and name the law that
supports your conjecture.
ANSWER:
Chloe will visit her grandma; the Law of Detachment.
QUESTION:
Is the conjecture Valid or Invalid?
If a polygon has three sides, then it is a triangle.
If a triangle has a 90 degree angle, then it is a
right triangle.
Conjecture: If a polygon has three sides, then it
is a right triangle.
ANSWER:
Invalid—misapplication of the law of syllogism.
QUESTION:
Write the contrapositive and the biconditional form of the
statement below. State whether each is true or false (if
false, give a counterexample)
If ∠𝐴 and ∠𝐵 are vertical, then ∠𝐴 and ∠𝐵 are ≅.
ANSWER:
Contrapositive: If ∠𝐴 and ∠𝐵 are not ≅, then ∠𝐴 and ∠𝐵
are not vertical. (TRUE)
Biconditional: ∠𝐴 and ∠𝐵 are vertical IFF ∠𝐴 and ∠𝐵 are ≅.
(FALSE ∠𝐴 and ∠𝐵 don’t have to touch)
QUESTION:
Name the two tools used in geometric
constructions.
ANSWER:
Compass and straightedge
QUESTION:
Jerry is in the process of doing the angle bisector
construction. His work is shown below. What
should be his next step?
ANSWER:
Create a ray starting at the vertex, through
the intersection of the arcs.
QUESTION:
Which construction is shown below?
ANSWER:
Perpendicular Bisector
QUESTION:
Draw an obtuse angle and copy it
(construction).
ANSWER:
QUESTION:
Construct a 45 degree angle.
ANSWER:
Perpendicular bisector, angle bisector.
QUESTION:
What is the property illustrated below:
𝑎 = 𝑏,
𝑏=𝑎
ANSWER:
Symmetric Property
QUESTION:
What is the definition that would be a
reason for the following:
𝐴𝐵 ≅ 𝑀𝑁 therefore 𝐴𝐵 = 𝑀𝑁.
ANSWER:
Definition of congruent segments
QUESTION:
Provide a reason for the statement below:
𝑚∠𝐷𝐹𝐺 + 𝑚∠𝐺𝐹𝐻 = 𝑚∠𝐷𝐹𝐻 Angle Add. Post.
2𝑛 + 6𝑛 − 4 = 180
ANSWER:
•Substitution
?????
QUESTION: Toby needs help writing a proof to
show that 𝑚∠𝐷𝐹𝐺 = 46°. Complete his proof.
Statements
Reasons
1. ∠𝐷𝐹𝐻 is a straight angle;
1.
𝑚∠𝐷𝐹𝐺 = 2𝑛, 𝑚∠𝐺𝐹𝐻 = 6𝑛
2. 𝑚∠𝐷𝐹𝐺 + 𝑚∠𝐺𝐹𝐻 = 𝑚∠𝐷𝐹𝐻 2. Angle Add. Post.
3.
2𝑛 + 6𝑛 − 4 = 180
3.
4.
5.
6.
7.
8.
𝑛 = 23
4. Simplify
5.
6.
7. Substitution
8. Simplify
𝟏
𝟐
QUESTION: Prove the following:
If 𝑚∠1 = 5𝑥 + 70 and 𝑚∠2 = 12𝑥 + 35, then 𝑚∠1 = 95°
Statements
1.
2.
3. 𝑚∠1 = 𝑚∠2
Reasons
1.
2. Vertical Angles Thm.
3.
4. 5𝑥 + 70 = 12𝑥 + 35
5.
6.
4.
5.
6.
7.
8.
7. Division Prop. =
8.
9.
9.
QUESTION:
•Type your question in here relating to Topic 5. As the Points
get higher make questions harder.
ANSWER:
•(type answer here)
QUESTION:
•Type your question in here relating to Topic 5. As the Points
get higher make questions harder.
ANSWER:
•(type answer here)
QUESTION:
•Type your question in here relating to Topic 5. As the Points
get higher make questions harder.
ANSWER:
•(type answer here)
QUESTION:
•Type your question in here relating to Topic 5. As the Points
get higher make questions harder.
ANSWER:
•(type answer here)
QUESTION:
•Type your question in here relating to Topic 5. As the Points
get higher make questions harder.
ANSWER:
•(type answer here)