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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)”. |
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| 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 and the figure below, use of the distance formula to 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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| 5) In a triangle, what is an included angle? |
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| Activity: Print out Triangle PQR. Use a compass and straightedge to construct congruent triangle XYZ applying the SAS postulate. |
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| 8) In the previous construction, explain how you constructed the included angle. |
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| 9)
Write a paragraph proof OR type up a formal proof with statements and reasons for the given information and the figure below. You may enter your proof in the textbox below or prepare it in a word-processing document and attach the file. (Hint: First prove how triangles ABD and BCD are congruent using SAS, and then apply CPCTC.) |
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| The next proof requires several reasons that are theorems, postulates, and definitions studied in previous units along with new ones presented in this unit. Review the following theorems and definitions: Theorem 5-E, Theorem 7-J, Theorem 8-A, and CPCTC. |
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| 10)
Copy or print out the partial proof of the given information and the figure shown below. Complete the proof, and then state the number of the missing reason and the corresponding answer.
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| 11) In a triangle, what is an included side? |
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| 15) Copy or print out the partial proof of the given information and the figure shown below. Complete the proof, and then state the number of the missing statement or reason and the corresponding answer. |
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| Refer to the figure below to answer the next three questions. |
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| 18)
Refer to the figure below and write a paragraph proof to prove that segments PR and QS are congruent. Build the proof around the AAS Theorem. |
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| Isosceles and Equilateral Triangles |
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| 19) 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 of isosceles triangle JKL shown below to answer the next six questions. We will use some creative thinking to prove this theorem. |
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| 21) 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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| 24) Finally, you can say that angle L is congruent to angle K because of what rule used in geometry? |
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| 25) In the previous proof, segment JM is called an “auxiliary line segment”. In your own words, write a definition of an “auxiliary line segment”. |
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| 26) Write a paragraph proof similar to the proof of Theorem 11-B in the previous questions. An auxiliary line segment is provided in the figure below to help with the proof. An angle bisector (segment JM) of angle J is “added” to triangle JKL. Use the definition of angle bisector to build your proof. |
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| Refer to the figure below to answer the next three questions. |
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| 29) Answer the following questions: (a) What is the value of “x”? (b) Angle 1 measures how many degrees? (c) Angle 2 measures how many degrees? |
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| 32) Which postulate or theorem could be used to deduce that the two triangles are congruent? |
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| 33) Which postulate or theorem could be used to deduce that the two triangles are congruent? |
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| 34) Which postulate or theorem could be used to deduce that the two triangles are congruent? |
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| For the next six problems refer to the figure and information given below. Notice that a disclaimer is attached to the figure. Make sure that you answer the questions based on the given information, not the appearance of the figure. Support your answers with postulates, definitions, theorems and/or corollaries. |
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| 35) What is the measure of angle ANC? Give a reason to support the answer. |
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| 36) What is the measure of angle BCA? Give a reason to support the answer. |
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| 37) What is the measure of angle 2? Give a reason to support the answer. |
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| 38) What is the measure of angle 4? Give a reason to support the answer. |
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| 39) What is the measure of angle AJN? Give a reason to support the answer. |
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| 40) What is the measure of angle BJN? Give a reason to support the answer. |
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| 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 DEH is congruent to triangle FEG. Refer to the information and figure given below. Submit a word-processing document to your instructor via VLA email. |
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| 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 make a structure firm. Submit a document to your instructor either describing the three instances of a triangle in use and/or showing it in use through a picture or diagram. |
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| 41) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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| No offline activities found |
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