BATAC NATIONAL HIGH SCHOOL Poblacion Campus SY 2014 – 2015 THIRD PERIODIC EXAMINATION MATHEMATICS 8 Name:____________________ Name:_________________________________ __________________________ _______________________________ _______________________________ _____________________Gr. ________Gr. &Sec.:_______________ &Sec.:____________________________ _____________________Sco ________Score:___________ re:_________________ ______
Part I. Multiple Choice. Write the letter of choice that best completes the statement or answers the question before number. 1.
Determine the hypothesis of the statement, ” If the baby is wearing blue booties, then it is a baby boy .” A. B. C. D.
2.
What is the conclusion of the statement, “ If the light is red, then you must stop.”? A. B. C. D.
3.
the light is red if the light is red you must must stop. then you must stop
Which statement is a counterexample for the following statement, “ If Carl studies at least two hours for the test, then Carl will pass.”? A. B. C. D.
4.
if the baby is wearing blue booties the baby is wearing blue booties then it is a baby baby boy it is a baby boy
Carl studied only 30 minutes and Carl passed passed the test. Carl studied 3 hours for the test test and Carl did not pass. Carl studied one hour for the test and Carl did not pass. Carl studied for 2 hours and pass the test.
Write this statement as a conditional in if-then form: All triangles have three sides. A. If a triangle has three sides, then all triangles have three sides. B. If a figure has three sides, then then it is not a triangle. C. If a figure is a triangle, then all triangles have three sides. D. If a figure is a triangle, then it has three sides.
5.
Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ and the part following then is the ____. A. B. C. D.
6.
conditional; conclusion; hypothesis conditional; hypothesis; conclusion hypothesis; conclusion; conditional hypothesis; conditional; conclusion
Which statement is a counterexample for the following conditional? If you live in Batac City, then you live in Ilocos Norte. A. Sara Lucas lives in Batac City. B. Jonah Lincoln lives in Batac City, Ilocos Norte. C. Billy Jones lives in Paoay, Ilocos Norte. D. Erin Naismith lives in Ilocos Norte.
7.
What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. positive. a. If a point is in the first quadrant, then its coordinates are positive. b. If a point is not in the first quadrant, then the coordinates of the point are not positive. c. If the coordinates of a point are positive, then the point is in the first quadrant. d. If the coordinates of a point point are not positive, then the the point is not in the first quadrant.
9.
Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively ."? deductively ."? A. If you reason deductively, then you understand geometry. B. If you understand geometry, then you reason deductively. C. If the do not reason deductively, then you understand geometry. D. If you understand deductively, then you reason geometry.
10. It is a mathematical statement accepted as true without any proof. A. B. C. D.
postulate definition theorem law
11. “An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.”, is an example of _____________. A. B. C. D.
law axiom definition postulate
12. Which of the following illustrates a theorem? A. An acute triangle is a triangle with all three angles less than 90°. B. If two lines intersect, then they intersect in exactly one point. C. Through any three noncollinear points, there is exactly one plane. D. A line contains at least two points 13. Use the information given in the diagram. Tell why A
and A. B. C. D.
Reflexive Property, Given Transitive Property, Reflexive Property Given, Reflexive Property Reflexive Property, Transitive Property
14. State whether your answer.
and
D
C
are congruent. Justify 7
A. B. C. D.
B
7
yes, by either SSS or SAS yes, by SSS only yes, by SAS only No; there is not enough information to conclude that that the triangles are congruent
15. Which overlapping triangles are congruent by AAS? A. B. C. D.
8.
When a conditional and its converse are true, you can combine them as a true ____. A. counterexample B. unconditional C. biconditional D. hypothesis
16. The sides of an isosceles triangle have lengths , . The base has length . What is the length of the base? A. 18
B. 4
C. 12
D. cannot be determined
17. ∆ABC≅∆A’B’C’, m∡C = 3x – 40 and m ∡C’ = 2x – 10. Determine the ∡C’. A. 15
B. 30
C. 50
__________3.
__________4.
D. 90
18. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m ∠ACB. A. m∠ACB = 77° B. m∠ACB = 67° C. m∠ACB = 23° D. m∠ACB = 113°
__________5.
___________6.
19. According to the construction shown in the diagram below, what do we call segment ̅ ? A. B. C. D.
bisector of angle C median to side perpendicular bisector of segment altitude to side
Part IV. Match the given statements from the terms inside the box. Write the letter of choice before the number.
20. ΔABD ≅ ΔCBD. Name the theorem or postulate that justifies the congruence. A. B. C. D.
AAS SAS HL ASA
1. 2.
̅ is the perpendicular bisector of 21. In the diagram below, GH. Then ∠KGF ≅ ________.
A. B. C. D.
A. Theorem
3. 4. 5. 6.
∠FKG ∠KF
B. Postulate
C. Definition
A right triangle is a triangle that has a right angle. An angle is the inclination to one another of two straight lines that meet. If equals are joined to equals, the wholes will be equal. Vertical angles are equal in measure. For any segment, the measure of the whole is equal to the sum of the measures of its non-overlapping parts. If two parallel lines are intersected by a transversal, then alternate exterior angles are equal in measure.
∠KHF
Part V – A. Direct Proof.
∠KFH
Given: ∆ABC is an acute triangle. Prove: m∠A < 90.
Part II. True or False. Write the name of your “CRUSH” if the statement is true before the number. Otherwise, write the name of your “FAVORITE TEACHER”. ________________________1. If a deductive argument has true premises and a false conclusion, then it must be invalid. ________________________2. If the conclusion of an argument follows from the definition of a word used in a premise, then the argument is deductive. ________________________3. Because triangle A is congruent with triangle B, and triangle A is isosceles, it follows that triangle B is isosceles. This passage can be described as inductive argument. ________________________4. If there is a general statement in the premises, the argument will always be inductive. ________________________5. Arguments that have a time sequence in the premises (A happened, B happened) and a causal statement in the conclusion (A caused B) will always be inductive.
B
A
C
Proof:
Statements
Reasons
Part V – B. Proving Triangle Congruence
Part III – A. Identify the term/terms being describe by each statement. _________________________1. It is the "if" statement of a theorem. _________________________2. A mathematical argument that starts from a general premise to a particular premise. _________________________3. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. _________________________4.
Takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another
Part III – B. Identify the Triangle Congruence Postulate that is applied in the following illustrations. Write your answer before the number. _________1.
__________2.
Statements
Reasons
Part V – C. Proving Triangle Congruence
Part VI – Writing Mathematically. Given the conditional statement, “ If you get good grades then you will get into a good college.”, give its converse, inverse and its contrapositive. Converse:
Statements
Reasons _______________________________________________________________________________ _______________________________________________________________________________ _____________________________________________________________________________
Inverse: _______________________________________________________________________________ _______________________________________________________________________________ _____________________________________________________________________________
Contrapositive: _______________________________________________________________________________ _______________________________________________________________________________ _____________________________________________________________________________
“ A
man who lies to himself, and believes his own lies become unable to recognize truth, either in himself or in anyone else, and he ends up losing respect for himself and for others. When he has no respect for anyone, he can no longer love, and, in order to divert himself, having no love in him, he yields to his impulses, indulges in the lowest forms of pleasure, and behaves in the end like an animal. And it all comes from lying – lying to others and to yourself.” sirjj1131987 #pusong bato
