Download If two angles are congruent, they are right angles

GROUP 2
NAME :
1.USWATUN KHASANAH
2.TIKA NURLAELI
3.SITI AMIDAH
4.NURFETI DWI SUSILOWATI
Page 77
7. Identify the hypothesis and conclusion in the
following:
a. Two lines are parallel if they do not intersect
conclusion
hypothesis
b. All squares are rectangles
hypothesis
conclusion
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2. Produce a counterexample for the following false
generalization.
There is only one line perpendicular to a given line at
a point on that line.
False generalization : There is only one line
perpendicular to a given line at a point on that line.
Comment
: to show that the
generalization is false, we must provide not only one
line perpendicular to a given line at a point on that
line.
Counterexample
: figure ab and cd are
perpendicular, but not only cd which can
perpendicular with ab, ef and ab are perpendicular too
4. True – false
a. Two points determine a line (true)
b. A line separates space into two half-spaces
(false)
c. If two planes intersect, the intersection is a point
(false)
d. If X, Y, and Z are collinear and XZ + ZY = XY
then Z is between X and Y (true)
5. If B is between A and C, AC = 10, and
AB = 4, find BC.
Answer:
BC
= AC – AB
= 10 – 4
=6
7. Identify the hypothesis and conclusion in the following
statements:
a. A triangle is isosceles if it has two congruent sides
conclusion
hypothesis
a. All equilateral triangles have three congruent angles
hypothesis
conclusion
8. Consider the statement:
If two angles are right angles, they are congruent.
a. Write the converse statement
Answer:
If two angles are congruent, they are right angles.
b. Write the inverse statement
Answer:
If two angles are not right angles, they are not
congruent.
c. Write the contapositive statement
Answer:
If two angles are not congruent, they are not right
angles
d. Produce counterexamples to show a and b are false
If two angles are congruent, they are right angles.
False generalization
: If two angles are congruent, they
are right angles.
Comment
: to show that the generalization is
false, we must provide two angles are congruent which does not
right angle.
Counterexample
: figure ⦟abc and ⦟klm are
congruent but they are not right angle, they are acute angle.
c
m