MULTIPLE CHOICE
Which of the following is the correct conclusion from the statement: "If it is raining, then the ground will be wet"?
A. If the ground is wet, it is raining.
B. If the ground is not wet, it is not raining.
C. If the ground is wet, it could be raining.
D. The ground will be wet if it is not raining.
B. If the ground is not wet, it is not raining.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
Statement 1: If a triangle has an interior angle of 90°, then it is a right triangle.
Statement 2: If a triangle is a right triangle, then it has an interior angle of 90°.
A – Statement 1 is true, and Statement 2 is true.
Tell whether each statement is always true, never true, or sometimes true.
Two points in a plane are collinear.
always true
Inverse: If two triangles are not congruent, then their corresponding sides and angles are not equal.
Make a converse statement:
If the corresponding sides and angles are not equal, then two triangles are not congruent.
If ∠ABC is a right angle, m∠ABD = (2x − 12) °, and m∠DBC =(2x + 10) °. Find m∠ABD.
(2x−12)+(2x+10)=90 ; m∠ABD=34°
What is the relationship between the statements below?
Statement 1: If a quadrilateral is a rhombus, then it has four congruent sides.
Statement 2: If a quadrilateral is not a rhombus, then it does not have four congruent sides.
A. Statement 2 is the inverse of statement 1.
B. Statement 2 is the converse of statement 1.
C. Statement 2 is the biconditional of statement 1.
D. Statement 2 is the contrapositive of statement 1.
A. Statement 2 is the inverse of statement 1.
Use inductive reasoning to make a conjecture about the next item in the pattern and what the pattern is.
1/3, 2/3, 1, 4/3, 5/3, 2, ______
7/3
Tell whether each statement is always true, never true, or sometimes true.
If ∠F and ∠G are supplementary angles, then m∠F = 90°.
sometimes true.
What property is being applied if KL=KL?
Given line segment QR is congruent to line segment ST. If QR = 2/3 x in. and ST = 0.4 in., what is the value of x?
2/3x = 0.4 ; x = 3/5 or 0.6
If ∠Q and ∠R are a linear pair and m∠R = 136°, what is m∠Q in degrees?
A. 44°
B. 43°
C. 42°
D. 41°
A. 44°
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
Statement 1: If a figure has four sides of equal length, it is a square.
Statement 2: If a figure is a square, then all four sides are equal in length.
C – Statement 1 is false, and Statement 2 is true.
Tell whether each statement is always true, never true, or sometimes true.
A point has length.
never true
Contrapositive: If you study hard, then you will pass the exam.
Make an inverse statement:
If you did not study hard, then you will not pass the exam.
Three lines intersect at the same point to form angles. If m∠B = 17° and m∠C = 21°, what is m∠A in degrees?
m∠A+17+21=360 ; m∠A = 322°
Which statement is a counterexample to the statement below? If ∠A and ∠B are supplementary angles, then m∠A ≠ m∠B
A. Angle A is an obtuse angle.
B. Angle A is a straight angle.
C. Angle B is an acute angle.
D. Angle B is a right angle.
A. Angle A is an obtuse angle.
Use inductive reasoning to make a conjecture about the next item in the pattern and what the pattern is.
CH4, C2H6, C3H8, C4H10, _________
C5H12
Tell whether each statement is always true, never true, or sometimes true.
If ∠M and ∠N are complementary angles, then m∠M > m∠N.
sometimes true
If line segment JK is congruent to line segment LM, therefore, in what reason will state that JK is equal to LM?
Definition of Congruent Segments
Angle X and angle Y are complementary angles and ∠Y ≅ ∠Z. If m∠X = (9x + 4)° and m∠Y = (21x − 34)°, what is m∠Z in degrees?
(9x+4)+(21x−34)=90;
∠Y ≅ ∠Z ; 21x−34=21(4)−34=84−34=50
m∠Z = 50°
Which of the following best describes the deductive method in geometry?
A. It involves making generalizations based on specific observations or examples.
B. It uses known facts, definitions, and logical reasoning to prove new statements or theorems.
C. It relies on empirical testing and experiments to verify geometric principles.
D. It involves constructing geometric figures to visualize relationships and conjectures.
B. It uses known facts, definitions, and logical reasoning to prove new statements or theorems.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
Statement 1: If two lines are parallel, then they do not intersect.
Statement 2: If two lines do not intersect, then they are parallel.
B – Statement 1 is true, but Statement 2 is false.
Tell whether each statement is always true, never true, or sometimes true.
Line XY is longer than segment XY.
always true
Conditional: If two lines are parallel, then they do not intersect.
Make a contrapositive statement:
If they did intersect, then two lines are not parallel.
Three lines intersect at the same point to form angles. If m∠Y = 33° and m∠Z = 87°, what is m∠X in degrees?
m∠X +33+87=360 ; m∠X = 240°