3rd Periodical Examination
Mathematics 9 (R)
C.Y. 2015-2016
Name: ____________________________
Grade and Section:__________________
Date: _______ Points: _____ Item: 70
Direction: Write the word True if the statement is correct and False if not.
Special Parallelograms
__________ 1. A quadrilateral with four congruent sides is a rhombus.
__________ 2. A parallelogram with at least one right angle is a rectangle.
__________ 3. A quadrilateral with perpendicular diagonals is a rhombus.
__________ 4. A quadrilateral with congruent diagonals is a rectangle.
__________ 5. If the diagonals of a quadrilateral bisect each other, then the quadrilateral
is a rectangle.
__________ 6. If the diagonals of a quadrilateral are perpendicular bisector of each other,
then the quadrilateral is a rhombus.
__________ 7. If all angles of a quadrilateral are congruent, then the quadrilateral is a
rectangle.
__________ 8. Every square is a rhombus.
_________ 9. All squares are rectangles.
_________ 10. Some rectangles are rhombi.
Direction: For each item, choose the best answer.
Quadrilaterals
__________ 11. Which of the following is not true about a parallelogram?
A. Opposite sides are congruent.
B. Adjacent sides are congruent.
C. Opposites angles are congruent.
D. Opposite sides are parallel.
E. Diagonals bisect each other.
__________ 12. A quadrilateral is a parallelogram if
A. diagonals are perpendicular
B. diagonals are congruent
C. two adjacent sides are congruent
D. adjacent angles are supplementary
E. a diagonal forms two congruent triangles
__________ 13. Which of the following is not true about a rectangle?
A. The diagonals are congruent.
B. All angles are congruent.
C. The diagonals bisect each other.
D. The diagonals are perpendicular.
E. Adjacent angles are supplementary.
__________ 14. Which of the following is not sufficient to prove that a parallelogram is a
rectangle?
A. The diagonals are congruent.
B. The diagonals are perpendicular.
C. Two adjacent angles are congruent.
D. One angle is a right angle.
E. All angles are congruent.
__________ 15. Which of the following is sufficient to prove that a quadrilateral is a rhombus?
A. The diagonals are congruent.
B. The diagonals bisect each other.
C. The diagonals are perpendicular.
D. Each diagonal is a perpendicular bisector nor the other.
E. Two adjacent sides are congruent.
Direction: Reduce each ratio to its lowest term. ( 2 points each )
Ratio and Proportion
16.
3
12
=
17.
8
24
=
18.
35
50
=
19.
15
60
20.
2a 2
4a
=
=
Direction: Tell whether two figures of the given types are always, sometimes, or never similar.
Similar Triangles and Polygons
__________ 21. rectangles
__________ 22. squares
__________ 23. triangles
__________ 24. right triangles
__________ 25. equilateral triangles
__________ 26. circles
__________ 27. equilateral triangles
__________ 28. isosceles trapezoids
__________ 29. regular nonagons
__________ 30. a right triangle and an equilateral triangle
Direction: Find the length of the hypotenuse of an isosceles right triangle when the length of a
leg is __ ( 2 points each )
Other Theorems on Right Triangles
31. 17
= __________
32. 13
= __________
33. 0.75 = __________
34. 0.5
= __________
35.
= _________
5
Direction: Identify the following.
36. A triangle, all of whose angles are acute, is ____________________.
37. The perpendicular sides in a right triangle are called ____________________.
38. The hypotenuse in ∆PQR if mR = 90 is ____________________.
39. What kind of angles are P and Q in #3? ____________________.
40. A perpendicular segment from the vertex of the triangle to the line containing the
opposite side is called ____________________.
41. A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite
side is called ____________________.
42. The point of concurrency of the three medians of a triangle is called ________________.
43. The point of concurrency of the three altitudes of a triangle is the ___________________.
44. The sum of the measures of the three angles of any triangle is ____________________.
45. A triangle where the altitude is also the median and the angle bisector is called ________.
Direction: Fill in the blanks.
A. Given: 2  4
J
3  1
1
E
2
Prove: ET  SJ
4
Proof:
3
S
Statements
T
Reasons
41. 2  4
__________________________________________
42. 3  1
__________________________________________
43. JT  JT
__________________________________________
44. ∆ JET  ∆TSJ
__________________________________________
45. ET  SJ
__________________________________________
B. How many sides does a regular polygon have if the measure of each exterior angle is
45?
Solution: The measure of each exterior angle is ___
n
360 = _________
n
45 n = _________
n = _________
Thus, the polygon has __________ sides.
Direction: Draw and interpret the following theorems using symbols and markings. ( 5 points
each )
A. Transversal and Parallel Lines.
Theorem 4.41
If three parallel lines intercept congruent segments on traversal t, then they will
intercept congruent segments on every transversal parallel to t.
B. Trapezoids
Theorem 4.61
The midline of a trapezoid is parallel to its bases, and its length is half the sum
of the lengths of the bases.
C. Proving Similar Triangles
The AAA Similarity Postulate
If the three angles of one triangle are congruent to three angles of another triangle,
then the two triangles are similar.
Goodluck and God Bless… 
Prepared by:
Julius John L. Palacpac
Math Teacher - Grades 3, 5, 7 and 9
jjlpalacpac@neu.edu.ph