Writing a Proof

A chain of justified steps.

12 problems · about 22 minutes · G-CO.C.10, G-SRT.B.4

NameDate

Figure — use these to answer the problems

A proof about this triangle may use only stated facts, never how the drawing happens to look.

One leg6

Other leg8

Figure 1

Straightforward practice. Get the method working first.

5 problems

Three pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer
2
Why can a diagram not justify a step?
- Appearance is not evidence; only stated or derived facts count.
- Because diagrams are never to scale.
Is "the diagram looks that way" a valid reason? 1 yes, 0 no.
Answer
Is a previously proved theorem a valid reason? 1 yes, 0 no.
Answer
Two triangles with two equal sides and an equal included angle. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer

The same ideas with more to keep track of.

3 problems

How many statements in a two-column proof need a reason?
Answer
A triangle has angles 70° and 60°. Third angle, in degrees?
Answer
Once two triangles are congruent, are corresponding parts equal? 1 yes, 0 no.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Put the proof-writing process in order.
Write 1 to 4 in the boxes to put these in order.
- Read the given information and the conclusion wanted.
- Work backwards to find what would give that conclusion.
- Write the statements forwards from the given facts.
- Attach a reason to every statement.
Two angles and the included side equal. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer
The Shared Side
A side shared by two triangles is equal to itself. How many pairs of equal sides does that supply?
Answer
The Criterion
Three pairs of equal sides. Which criterion? 1 SSS, 2 SAS, 3 ASA.
Answer