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Triangle Congruence Proofs Review Game

Date post: 25-Oct-2015
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This is a simple game to get students to practice triangle congruence proofs. Students start with the page that has "RP" in the upper right hand corner. They do the proof and find the answer to that proof on a different sheet of paper. On the back of the answer is another problem for the students to complete, then students search out the answer to the new problem and repeat the procedure. At the end, if they've kept track of the order they worked the problems in, they can place all the letters in order, unscramble them and a message appears.
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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) _____________________________________ R
Transcript
Page 1: 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) ___________________________________________

R

Page 2: Triangle Congruence Proofs Review Game

ANSWERS

Page 3: Triangle Congruence Proofs Review Game

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

O

Page 4: Triangle Congruence Proofs Review Game

ANSWER:

AND

Page 5: Triangle Congruence Proofs Review Game

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

Page 6: Triangle Congruence Proofs Review Game

ANSWER

Page 7: Triangle Congruence Proofs Review Game

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?

________________________________

________________________________

________________________________

AN

Page 8: Triangle Congruence Proofs Review Game

ANSWER

Page 9: Triangle Congruence Proofs Review Game

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

Page 10: Triangle Congruence Proofs Review Game

6.____________________________________________________________________The

n, ____________________________________________________________________

7.____________________________________________________________________Fina

lly, ___________________________________________________________________

ANSWER

Page 11: Triangle Congruence Proofs Review Game

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

T

Page 12: Triangle Congruence Proofs Review Game

ANSWER

Page 13: Triangle Congruence Proofs Review Game

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