triangle congruence proofs review game

1. Use the figure at the right. How can you prove that ΔGMH ΔTMS? Justify each step.

Given: M is the midpoint of and .

Prove: ΔGMH ΔTMS

1) M is the midpoint of and . 1) _______________________________________

2) 2) _______________________________________

3) 3) _______________________________________

4) GMH TMS 4) _______________________________________

5) ΔGMH ΔTMS 5) _______________________________________

2. Use the figure at the right. How can you prove that ΔGHI ΔJHI?

Justify each step.

Given: H is the midpoint of .

Prove: ΔGHI ΔJHI

1) H is the midpoint of . 1) ___________________________________________

2) 2) ___________________________________________

3) 3) ___________________________________________

4) 4) ___________________________________________

5) ΔGHI ΔJHI 5) ___________________________________________

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ANSWERS

Study this example then complete the proof below in the same way.Given: The figure at the rightProve: ∆ ABQ≅ ∆ XYQ

Explain Work Justify

First, list the information that is given directly in the diagram. A and X

are right .

Given

Second, use the fact that all right angles are congruent to each other.

A X All right angles are congruent.

Next, use the fact that vertical angles are congruent.

AQB XQY Vertical Angles

Finally, determine which theorem can be used to prove the triangles congruent using the information listed above.

ΔABQ ΔXYQ Angle-Angle-Side (AAS) Theorem

Given: The figure at the rightProve: ∆ JHL≅ KLJ

Explain Work Justify

HJL KLJ

HLJ KJL

ΔHJL ΔKLJ

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ANSWER:

AND

There are two sets of note cards below that show how to prove is the perpendicular bisector of . The set on the left has

the statements and the set on the right has the reasons. Write thestatements and the reasons in the correct order.

S

Statements Reasons

Statements Reasons

ANSWER

The column on the left shows the steps used to prove that . Use thecolumn on the left to answer each question in the column on the right

in Right Triangles

Given: C is the midpoint of and

Prove: AB ED

1. What is the definition of the midpoint of a line segment?

________________________________

________________________________

________________________________

1) C is the midpoint of and ;

; mB = 90

Given

2. How do you know that and mB = 90?

_________________________________

2) ;Definition of midpoint

3. What does the symbol between two line segments mean?

________________________________

3) B = DAlternate Interior Angles Theorem

4. What does the word interior mean?

________________________________

4) B and D are right angles.

Definition of a right angle

5. What is the measure of D?

_________________________________

5) ∆ABC ∆EDCHypotenuse-Leg (HL) Postulate

6. What information is necessary to apply the HL Postulate?

________________________________

________________________________

________________________________

6)Corresponding parts of congruent triangles are congruent.

7. What are the corresponding angles and sides for ∆ABC and ∆EDC?

________________________________

________________________________

________________________________

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ANSWER

A student wanted to prove given

AED CDE and . She wrote the statements and reasons on note cards, but they got mixed up.

Use the note cards to write the steps in order.

1.____________________________________________________________________First

, _____________________________________________________________________

2.____________________________________________________________________Sec

ond,__________________________________________________________________

3.____________________________________________________________________Thir

d, ____________________________________________________________________

4.____________________________________________________________________Nex

t, ____________________________________________________________________

5.____________________________________________________________________The

n, ____________________________________________________________________

UH

6.____________________________________________________________________The

n, ____________________________________________________________________

7.____________________________________________________________________Fina

lly, ___________________________________________________________________

ANSWER

In each of the following three problems, the student made at least one error. Find the error and write the solution correctly.

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ANSWER