Unit 7 Leveled Skills Review – Isosc. Triangle Proof (#2)
Directions: Start at the level that best matches your current skill set. Complete each of the questions on a separate
sheet of paper. If a level seems too easy or difficult, you may switch to a different level. Once you finish the level you’re
on, move on to the following questions.
Level 1:
1.
2.
3.
4.
5.
Level 2:
6.
7.
8.
9.
10.
11.
Level 3:
12.
13.
14.
15.
Level 4:
Decoding & Writing notation, Decoding & marking diagrams, Naming given information
Write one sentence - What information is “Given” in the problem above?
Write one sentence - What are you trying to prove in the problem above? Do not just recopy the notation.
Write one sentence - What does ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 mean?
̅̅̅̅ ⊥ 𝐵𝐷
̅̅̅̅ mean?
Write one sentence - What does 𝐴𝐶
If I tell you ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐷𝐶 , what markings can you add to the diagram?
Citing definition, Citing prior knowledge, Pairing a statement to a particular reason
What is the definition of a midpoint?
If I tell you D is the midpoint of AC, what information can you add to your diagram?
What is the “Reflexive Property?”
Write a statement about the diagram above using the Reflexive Property
What does “SAS≅” used to prove? What information do you need to give it as a reason?
What does “≅ ∆ → ≅ 𝑝𝑎𝑟𝑡𝑠" mean?
Matching statements to reasons, Reading proofs, Organizing information within a proof
In a proof, where does your given information usually go?
In a proof, where does your conclusion usually go?
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅ is given information in the problem above
True or False: 𝐴𝐵
If you struggle to write a proof from scratch, grab a template from the front for the problem above. Order the
statements & reasons in both the flowchart & 2-column format.
Writing a proof independently, Analyzing the structure of arguments in proofs
16. If you skipped #15 – Without using a template, write a proof of the problem above.
17. If you completed #15 – Which statements could have been ordered differently in your 2-column proof? Which
statements could not be placed in a different order?
Name: __________________________________ Date: __________ Period: ______ Template: Isosc. Triangle Proof (#2)
Reorder the statements & reasons below into a 2 column proof and a flowchart proof.
Statements
Reasons
Name: __________________________________ Date: __________ Period: ______ Template: Isosc. Triangle Proof (#2)
Reorder the statements & reasons below into a 2 column proof and a flowchart proof.
Statements
Reasons
KEY Isosc. Triangle Proof (#2)
Directions: Start at the level that best matches your current skill set. Complete each of the questions on a separate
sheet of paper. If a level seems too easy or difficult, you may switch to a different level. Once you finish the level you’re
on, move on to the following questions.
Level 1:
1.
2.
3.
4.
5.
Level 2:
Decoding & Writing notation, Decoding & marking diagrams, Naming given information
AC and BD are perpendicular (meet at 90 degrees), and D is the midpoint of AC
That the two sides of the triangle – AB and BC – are congruent.
That AB is an exact copy (congruent to) BC
That AC and BD are perpendicular
The congruence tic markings to lines AD and DC
Citing definition, Citing prior knowledge, Pairing a statement to a particular reason
1.
2.
3.
4.
5.
A point that divides a segment exactly in half
The congruence tic markings to lines AD and DC, since AC was divided into two equal parts
Any side or angle is congruent to itself
BD is congruent to BD
SAS≅ is used to prove that two triangles are congruent. You need both triangles to have two pairs of
corresponding congruent sides and a corresponding congruent angle in between.
6. ≅ ∆ → ≅ 𝑝𝑎𝑟𝑡𝑠 is shorthand for the idea that if you know two triangles are exact copies, then you know all of
their corresponding sides & angles are also congruent.
Level 3:
7.
8.
9.
10.
Level 4:
Matching statements to reasons, Reading proofs, Organizing information within a proof
Given information usually goes at the beginning
Your conclusion should go at the end, and should be the very last statement you are proving.
False: ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 is what you are trying to prove, and so it should be your conclusion
See attached sheet
Writing a proof independently, Analyzing the structure of arguments in proofs
11. See attached sheet
12. Following the lettering on the template: Given information (E and G) has to be mentioned sometime before the
theorems that follow (B and F); B, F, and D have to be stated before C, and C has to be stated before A.
Name: __________________________________ Date: __________ Period:_____
KEY Isosc. Triangle Proof (#2)
Reorder the statements & reasons below into a 2 column proof and a flowchart proof.
E
G
B
Statements
Reasons
F
C
E
B
G
F
D
C
A
NOTE: We use the notation ≅ ∆ → ≅ 𝑝𝑎𝑟𝑡𝑠 instead of CPCTC
A
D