MATH Integrated Math II  - Unit 13: Proving Triangles Congruent
SSS Postulate

1) What phrase does SSS represent?

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2) Fill in the blanks. Postulate 13-A (SSS Postulate): If the __________ of a triangle are congruent to the __________ of a second triangle, then the triangles are congruent.

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Activity: Print out Triangle JKL. Use a compass and straightedge to construct congruent triangle FGH applying the SSS postulate. Follow the steps outlined in the unit link to “Side-Side-Side Postulate (SSS)”.

3) In the previous activity, throughout the construction you made congruent line segments. How did you use the compass to measure the length of the line segments?

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4) Based on the given information, the figure below, and the use of the distance formula; answer the following questions: (a) What are the lengths of each side of triangle RST? (b) What are the lengths of each side of triangle JKL? (c) Are triangles RST and JKL congruent?

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SAS Postulate

5) In a triangle, what is an included angle?

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6) What phrase does SAS represent?

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7) Fill in the blanks. Postulate 13-B (SAS Postulate): If two sides and the __________ of a triangle are congruent to __________sides and the included angle of a second triangle, then the triangles are congruent.

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Activity: Print out Triangle PQR. Use a compass and straightedge to construct congruent triangle XYZ applying the SAS postulate.

8) In the previous construction, explain how you constructed the included angle.

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9) Copy or print out the partial proof of the given information and the figure shown below. Complete the proof, and then state each number of the missing reason and the corresponding answer.

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ASA Postulate

10) In a triangle, what is an included side?

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11) What phrase does ASA represent?

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12) Fill in the blanks. Postulate 13-C (ASA Postulate): If two angles and the included side of a triangle are congruent to the__________ and the __________ of a second triangle, then the triangles are congruent.

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13) What does CPCTC represent?

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14) Copy or print out the partial proof of the given information and the figure shown below. Complete the proof, and then state each number of the missing statement or reason and the corresponding answer.

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AAS Theorem

15) What phrase does AAS represent?

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16) Fill in the blanks. Theorem 13-A (AAS Theorem): If two angles and a non-included side of a triangle are congruent to __________ and a __________ of a second triangle, then the two triangles are congruent.

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17) Refer to the figure below and write a paragraph proof to prove that segments PR and QS are congruent.

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Isosceles and Equilateral Triangles

18) Answer the following questions about the information and figure shown below: (a) Name the vertex angle. (b) Name the two base angles. (c) Name the base. (d) Name the legs.

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Refer to the Isosceles Triangle Theorem and the figure below to answer the next six questions. We will use some creative thinking to prove this theorem.

19) What is given?

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20) Let point M be the midpoint of segment LK. (You are permitted to add to a diagram as long as the addition you make is true.) Draw a line segment from point J to point M. You can now say that segment LM is congruent to segment MK. What reason supports this statement?

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21) What postulate supports the statement below?

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22) Now, since you have proven that all three sides of triangle JML is congruent to all three sides of triangle JMK, what postulate supports the statement below?

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23) Finally, you can say that angle L is congruent to angle K because of what definition?

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24) In the previous proof, segment JM is called an “auxiliary line segment”. Write a definition of an “auxiliary line segment”.

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25) Fill in the blank: Theorem 13-C: If two angles of a triangle are congruent, then the __________ that are opposite those angles are congruent.

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26) Fill in the blank: Corollary 13-B-1: A triangle is equilateral if and only if it is __________.

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27) Fill in the blank: Corollary 13-B-2: Each angle of an equilateral triangle measures __________.

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Refer to the figure below to answer the next three questions.

28) Answer the following questions: (a) What is the value of “x”? (b) What is the value of angle 1? (c) What is the value of angle 3?

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29) Answer the following questions: (a) What is the value of angle 2? (b) What is the value of angle 4?

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30) Answer the following questions: (a) What is the value of angle 5? (b) What is the value of angle 6?

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Review

31) Which postulate or theorem could be used to deduce that the two triangles are congruent?

32) Which postulate or theorem could be used to deduce that the two triangles are congruent?

33) Which postulate or theorem could be used to deduce that the two triangles are congruent?

Extra Credit: Check with your instructor to see if he/she is interested in awarding extra credit to you for developing a two-column proof (with statements and reasons) to prove that triangle DAP is congruent to triangle LAN. Refer to the information and figure given below. Submit a word-processing document to your instructor via VLA email.

Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: A triangle is a rigid fixture used in constructing buildings, bridges, and other large structures. It is frequently used to reinforce frameworks. Look around your home and/or the Internet to find three instances of a triangle used to firm up a structure. Submit a document to your instructor either describing the three instances of a triangle in use or showing it in use through a picture or diagram.

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