Just some points for today
2 answers:
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<em><u>Question:</u></em>
Triangle DEF is congruent to right triangle GHI with a right angle at vertex H. If the slope of DE is –2, what must be true?
A. The slope of HI is 1/2.
B. The slope of EF is 1/2.
C. The slope of GH is –2.
C. The slope of DF is –2.
<em><u>Answer:</u></em>
The slope of HI is 1/2
The slope of EF is 1/2
<em><u>Solution:</u></em>
Given that,
Triangle DEF is congruent to right triangle GHI
Which means,
These pairs of angles are congruent
{D, G}, {E, H}, and {F, I}
In triangle DEF, E is a right angle
This means that the line segments are perpendicular.
We know that,
Product of slope of a line and slope of line perpendicular to that line is equal to -1
Given that,
Slope of DE = -2
Since the sides EF and HI are congruent,
Slopes of parallel lines are equal
Thus, Slope of HI is 1/2
Answer:
m∠QPM=43°
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠NPQ=m∠MPN+m∠MPQ
we have
m∠NPQ=(9x-25)°
m∠MPN=(4x+12)°
m∠MPQ=(3x-5)°
substitute the given values and solve for x
(9x-25)°=(4x+12)°+(3x-5)°
(9x-25)°=(7x+7)°
9x-7x=25+7
2x=32
x=16
Find the measure of angle QPM
Remember that
m∠QPM=m∠MPQ
m∠MPQ=(3x-5)°
substitute the value of x
m∠MPQ=(3(16)-5)=43°
therefore
m∠QPM=43°
