Parallel, Perpendicular, and All That
First, some vocab
Definition: A meaning to a word using previously defined 📕 words.
Definition: A meaning to a word using previously defined 📕 words.
Postulate or Axiom: A statement that's accepted to be true, but can't be proven 😲
Postulate or Axiom: A statement that's accepted to be true, but can't be proven 😲
Example: Exactly one line can be drawn through two points
Theorem: A statement that can be proven true using logical 🧠 arguments based on facts and statements
Theorem: A statement that can be proven true using logical 🧠 arguments based on facts and statements
Example: The diagonals of a square 🟩 are perpendicular
So, to recap:
Now the good stuff!
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example
congruent
is like the geometry version of equal
"Angle A is congruent to Angle B"
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
"Line Segment AB is congruent to Line Segment PQ"
congruent
is like the geometry version of equal
example #2
congruent
is like the geometry version of equal
"Line Segment AB is congruent to Line Segment PQ"
P.S. 🤫 When talking about length of a line segment, you don't have to put the segment symbol on top
congruent
is like the geometry version of equal
example #3
congruent
is like the geometry version of equal
A
B
C
D
congruent
is like the geometry version of equal
example #3
congruent
is like the geometry version of equal
A
B
C
D
congruent
is like the geometry version of equal
example #3
congruent
is like the geometry version of equal
A
B
C
D
Since \( \overline{AB} \) and \( \overline{CD} \) have the same # Tick Marks, they're congruent
congruent
is like the geometry version of equal
example #3
congruent
is like the geometry version of equal
A
B
C
D
\( \overline{AB} \cong \overline{CD} \)
congruent
is like the geometry version of equal
example #4
congruent
is like the geometry version of equal
A
B
C
D
\( \overline{AB} \cong \overline{CD} \)
congruent
is like the geometry version of equal
example #4
congruent
is like the geometry version of equal
A
B
C
D
\( \overline{AB} \cong \overline{CD} \)
\( \overline{AD} \cong \overline{BC} \)
congruent
is like the geometry version of equal
example #5
congruent
is like the geometry version of equal
congruent
is like the geometry version of equal
example #5
congruent
is like the geometry version of equal
Can you see 👀 what angles or segments are congruent? 🤔
congruent
is like the geometry version of equal
example #5
congruent
is like the geometry version of equal
\( \overline{BC} \cong \overline{EF} \)
congruent
is like the geometry version of equal
example #5
congruent
is like the geometry version of equal
\( \overline{BC} \cong \overline{EF} \)
\( \measuredangle B = \measuredangle E \)
congruent
is like the geometry version of equal
example #5
congruent
is like the geometry version of equal
\( \overline{BC} \cong \overline{EF} \)
\( \measuredangle B = \measuredangle E \)
\( \measuredangle C = \measuredangle F \)
collinear
means points on the same line 🤔
collinear
means points on the same line 🤔
collinear
means points on the same line 🤔
A
B
C
collinear
means points on the same line 🤔
A
B
C
collinear
means points on the same line 🤔
A
B
C
Points \(A, B,\) and \(C\) are collinear
collinear
means points on the same line 🤔
A
B
C
Not anymore😂
Now they're noncollinear
coplanar
means on the same plane 🤔
coplanar
means on the same plane 🤔
A
B
C
D
coplanar
means on the same plane 🤔
A
B
C
D
coplanar
means on the same plane 🤔
A
B
C
D
Points \(A,B,C,\) and \(D\) are coplanar
intersect
is when lines or planes cross
intersect
is when lines or planes cross
intersect
is when lines or planes cross
Lines \( S\) and \(R\) intersect at Point M
intersect
is when lines or planes cross
Lines \( S\) and \(R\) intersect at Point M
Two lines always intersect at a Point
intersect
is when lines or planes cross
intersect
is when lines or planes cross
Planes \( ABC\) and \(ABD\) intersect at Line \( AB \)
intersect
is when lines or planes cross
Planes \( ABC\) and \(ABD\) intersect at Line \( AB \)
Two planes will always intersect at a line
parallel
means lines that never intersect and are coplanar🤨
parallel
means lines that never intersect and are coplanar🤨
parallel
means lines that never intersect and are coplanar🤨
Line \( s \parallel \) Line \( r \)
parallel
means lines that never intersect and are coplanar🤨
Line \( s \parallel \) Line \( r \)
👇 Parallel Symbol
parallel
means lines that never intersect and are coplanar🤨
parallel
means lines that never intersect and are coplanar🤨
Plane \( R \parallel \) Plane \( S \)
perpendicular
is when two lines or planes intersect at a right angle
perpendicular
is when two lines or planes intersect at a right angle
perpendicular
is when two lines or planes intersect at a right angle
Line \( s \perp \) Line \( r \)
👇 Perpendicular Symbol
perpendicular
is when two lines or planes intersect at a right angle
perpendicular
is when two lines or planes intersect at a right angle
Plane \( R \perp \) Plane \( S \)
perpendicular
is when two lines or planes intersect at a right angle
Line \( s \perp \) Line \( r \)
skew
lines that are not coplanar and never intersect
skew
lines are not coplanar and never intersect
skew
lines are not coplanar and never intersect
Notice 👀 how lines \( AE \) and \( GF \) are
skew
lines are not coplanar and never intersect
Notice 👀 how lines \( AE \) and \( GF \) are
- Not Coplanar
skew
lines are not coplanar and never intersect
Notice 👀 how lines \( AE \) and \( GF \) are
- Not Coplanar
- Never Intersect
skew
lines are not coplanar and never intersect
Notice 👀 how lines \( AE \) and \( GF \) are
- Not Coplanar
- Never Intersect
- Run in different directions, unlike parallel lines
Now you try!
\( \parallel \) and \( \perp \)
Still Confused 🤔?
Watch the Answer Key!
Parallel, Perpendicular, and All That
By Refath Bari
Parallel, Perpendicular, and All That
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