| Classifying Triangles by Angles |
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| For the next four problems, select the type of triangle that matches the description of the angles in the triangle. |
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| 2) One angle in the triangle measures more than 90 degrees. |
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| 3) All the angles in the triangle measure 60 degrees. |
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| 4) One angle in the triangle measures exactly 90 degrees. |
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| 5) All the angles in the triangle measure less than 90 degrees. |
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| Classifying Triangles by Sides |
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| For the next three problems, select the type of triangle that matches the description of the sides of the triangle. |
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| 6) All of the sides of the triangle measure different lengths. |
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| 7) Two sides of the triangle are equal in length. |
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| 8) All the sides of the triangle are equal in length. |
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| Use the distance formula to determine what type of triangle is shown in the grid below, and then answer the two next questions. |
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| 9) Answer the following questions: (a) What is the length of QR? (b) What is the length of RS? (c) What is the length of QS? |
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| 10) Triangle QRS is what type of triangle? |
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| 11) Triangle PON is an isosceles triangle. Find the value of “x”, and then answer the following questions: (a) What is the value of “x”? (b) What is the length of NO? (c) What is the length of OP? (d) What is the length of PN? |
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| 12) Explain how you determined the value of “x” in the previous problem. |
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| Fill in the blanks for the next three questions. |
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| 16) Define remote interior angles, and then name the remote interior angles of exterior angle ABD in the figure below. |
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| Print out or copy the figure below, and then answer the next four questions. |
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| 17) Answer the following questions using three (3) letters to name the angles: (a) Name the remote interior angles for exterior angle 2. (b) Name the remote interior angles for exterior angle 3. |
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| 20) Which theorem supports the answers to the previous two problems? |
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| 21) Explain how you can deduce that triangle ABD is an obtuse triangle. |
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| 22) The figure below may be used in the proof of the Angle Sum Theorem. Line JL is drawn parallel to segment MN and is justified by the Parallel Postulate (8-D). State the Parallel Postulate. |
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| 23) Copy or print out the partial proof of the Angle Sum Theorem shown below. State each reason, providing the number of the statement, and then the corresponding reason. Select the reasons from the following list: Postulate 1-B, Theorem 7-B, Theorem 7-J, Substitution, Definition of congruent angles, and Definition of supplementary angles. One reason will be used twice. Note: This would be a good time to use the list of compiled postulates and theorems posted in this unit. |
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| 24) What is a corollary? |
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| Fill in the blanks for the next three questions. |
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| 28) Corollaries 10-A-1 through 10-A-4 can “easily” be proven by the Angle Sum Theorem. State the Angle Sum Theorem (Theorem 10-A). |
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| 29) Copy or print out the partial proof of Corollary 10-A-1 and fill in the statements. Then state each number and the corresponding missing statement. |
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| 30) Now it’s time for you to try a proof on your own. For Theorem 10-C write a paragraph proof OR type up a formal proof with statements and reasons. Refer to the given information and the diagram below. You may enter your proof in the textbox below or prepare it in a word-processing document and attach the file. |
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| Refer to the following diagram to solve the next two problems. |
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| 31) What theorem or corollary supports the equation shown below? |
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| 32) Answer the following questions: (a) What is the value of “x”? (b) What is the measure of angle UTV? (c) What is the measure of angle WVU? |
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| Refer to the figure given below to solve the next four problems. |
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| Activity: Copy or print out the figure below. Use a compass to construct a line that is a perpendicular bisector to segment PQ. Draw the perpendicular bisector above segment PQ and down to the segment, but not below it. Add two more line segments to the drawing to make two right triangles that are reflections of each other. Label the midpoint of segment PQ as point M and the shared vertex of both triangles, point R. |
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| 37) Refer to the two right triangles that are reflections of each other in the previous activity and make three statements of congruence about the triangles’ angles and/or segments. |
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| 38) Use a compass to draw two intersecting circles that have equal radii. Connect the centers of the two circles and one of the points of intersection with line segments. What kind of triangle have you just created? Give some reasons to support your answer. |
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| 39) Select the type of transformation shown. |
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| 40) Select the type of transformation shown. |
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| 41) Select the type of transformation shown. |
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| Refer to the diagram below to complete the statements of correspondence or congruence in the next six problems. |
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| 48) In the figure below, triangle ABC is congruent to triangle ADC. What is the statement of correspondence between the two triangles that is an application of Postulate 10-A, “Any segment or angle is congruent to itself”? |
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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: Scott Hagan is a living “barn” artist from Jerusalem, OH. Research the Internet to find information about him and how he is using geometry in his career. Make a one page report about him and include pictures of his work. To retrieve a picture from the Internet, right click on the picture, copy it, and then paste it into the document. List the websites that you used as references for your information and pictures. Send the document to your instructor via the VLA email. |
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| 50) 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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