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= Our GeoPedia...The source for all things related to Period 2 Geometry 2009-2010 = = = Midterm Exam Review

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MIDTERM 2010 REVIEW - The Last Call
Enter your 3 midterm review questions in the list below. Be sure to follow the directions provided on SchoolWires.

1. Chapter 4, Section 4.6. When doing triangle proofs, what reason would you give if two sides of the triangle are parallel? (Laura) Not sure what you mean since the sides of a triangle cannot be parallel. Do you mean an application of the midsegment which is parallel to the third side? 2. Chapter 5, Section 5.2. What is the easiest way to tell the difference between perpendicular bisectors and the altitude of a triangle? (Laura) One end point of an altitude is a vertex, not so for perpendicular bisectors. The altitude usually does not pass through the midpoint of the opposite side, the perpendicular bisector does. 3. Chapter 5, Section 5.3. When would the median of a triangle also be the perpendicular bisector? How could you tell which is which? (Laura) In an isosceles triangle the segment from the vertex to the base is all four special segments. All properties apply in this case. 4. 4.3-4.4. How does the hypotenuse leg theorem work? (David) Hypotenuse-leg is used to prove two RIGHT triangles are congruent. Normally, this configuration in a triangle would look like SSA; however, in a right triangle, because of the relationship among the 2 legs and the hypotenuse, just having a pair of congruent legs and the hypotenuses congruent is enough. 5. 4.4. Why doesn't SSA work in proving triangles congruent? (David) SSA doesn't fix the size and shape of the triangles. You can create two triangles with two pairs of sides congruent and the non-included angle congruent that are themselves NOT congruent. Try to sketch a counterexample. 6. 3.3 What is the easiest way to write out the equation of a line? (David) You need 2 things to write an equation of a line: slope and y-intercept. If you have these 2 values, you can just plug them into the slope-intercept form of an equation of a line. If you have either 2 points or one point and the slope, you can find the slope in the first case and then use point slope with one point and the slope. Point slope is y-y1 = m(x - x1). 7. Chapter 2, Section 1.2 If you have two perpendicular planes, plane A and plane B, are all the lines in plane A parallel to plane B? (Deandra) No. They could also be skew. 8. Chapter 3, Section 3.4 How can you tell the difference between substitution property and transitive property? For example, you are given that angle 1 is congruent to angle 2. Then, angle 2 is congruent to angle 3 through vertical angle theorem. Next, angle 1 is congruent to angle 3. You are substituting angle 1 in for angle 2, yet the answer is transitive property. (Deandra) Technically, there is no substitution property of congruence although you may see it used. Since you are working with congruent parts, you would have to use the transitive property of CONGRUENCE. 9. Chapter 4, Section 4.5 When completing a proof, why must we prove that something is equal and then say it is congruent, when congruent means the same thing as equal? (Deandra) Congruent and equal don't technically mean the same thing. Equality applies to the measures of two figures (measures are equal). Congruency applies to the figure itself and indicates that both the SIZE and SHAPE are the same. In a proof, it's typical to have to change from congruency to equality so that you can apply properties of numbers to complete the proof. You then would need to transition back to congruency to support the "prove" statement. 10. 2.1-2.2 What is the difference between a biconditional and a conditional? (Jason) A conditional statement is an "if-then" statement. A biconditional statement occurs when the conditional and it's converse are both true (i.e., it's a "two-way" street). If that's true, you can condense the 2 statements into one using If and Only If (iff). 11. 3.2 How do tou make a 2 column proof into a flow proof? (Jason) I'm not sure why you would want to convert the proof structure. Flow proof is just an alternate structure of proof like the paragraph proof. The flow proof works like a flow chart actually showing the path of the proof. To create it, you use the same ideas as the 2-column (statement supported by reason). 12. 2.3 What is the law of detachment? (Jason) If you have an if-then statement that's true (if something happens, then there is a consequence) and the hypothesis part is put forth as part of a second statement, then by the Law of Detachment, you can conclude that the consequence from the first statement will occur. Example, (1)If it rains at night, I won't be able to walk the dog. (2)It is raining tonight. (3)Therefore, I won't be able to walk the dog. 13. 3.2 how does theorem 3.2 (no name) work? (paige) Theorem 3.2 is a property of perpendicular lines. Basically, if you have 2 acute angles that are also adjacent and the non-adjacent sides are perpendicular, the angle formed would be a right angle. Therefore, those 2 original acute angles would have to be complementary. 14. 2.3 how can you differentiate the law of detachment and syllogism? (paige) Syllogism has the same structure as the transitive property. It connects 3 thoughts. Example, If it rains at night, I won't be able to walk the dog. If I can't walk the dog, the dog will have an accident in his crate. If it rains at night, the dog will have an accident in his crate. Compare this to the example in #12 above (Detachment). Look at structure. 15. 5.2-5.3 what's an easy way to remember the points of concurrency for medians, altiudes, perp. biscectors and angle bisectors? (paige) See #18 below. 16. 4.3 &4.4 I'm confused on the HL postulate, how do you use it?(jessi) See #4 above. 17. 2.1 What is the law of detachment?(jessi) See #12 above. 18. chapter 5 How can you remember the special segments and their points of concurrency? (jessi) You might want to try flashcards or creating a nmemonic device (like PEMDAS). Maybe we can come up with one in class! 19. 5.2- If the circumcenter (of perpendicular bisectors of a triangle) is equidistant from the vertices and the incenter (of angle bisectors of a triangle) is equidistant from the sides, in what situation would you find the incenter oppose to the circumcenter or vise versa? (Kayla) Not sure what you mean by "oppose." 20. 3.5- In what proofs would you use dual parallel and dual perpendicular theorems? (Kayla) You would use these 2 theorems not necessarily in a formal proof but as a way to prove lines parallel (like the converses of the parallel line theorems are used). 21. 5.3- How do you find the slope of an altitude? (Kayla) The altitude is perpendicular to the side opposite the vertex from which it originates. So if you can find the slope of that side, the slope of the perpendicular bisector is the opposite reciprocal of that ratio.

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Well, 20 of you have not contributed to the list above by the deadline. You can avoid a 0 (but one point late and no bonus) by still submitting questions. Many thanks to those of you who DID DO YOUR HOMEWORK. May you do well on the Midterm this Wednesday.