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.

Example: A 🔺 is a polygon with 3️⃣ sides.

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:

  • Definition: Come on 💁‍♂️
  • Postulate or Axiom: True, but can't prove 😔
  • Theorem: True, and can prove! 🤩

Now the good stuff!

5️⃣ is equal to 5️⃣

5️⃣ = 5️⃣

5️⃣ is equal to 5️⃣

5️⃣ = 5️⃣

🔳 is congruent to 🔳

🔳 ≅ 🔳

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

\measuredangle A = 50^{\circ}

👉

congruent

is like the geometry version of equal

example

congruent

is like the geometry version of equal

\measuredangle A = 50^{\circ}
\measuredangle B = 50^{\circ}

👉

congruent

is like the geometry version of equal

example

congruent

is like the geometry version of equal

\measuredangle A = 50^{\circ}
\measuredangle B = 50^{\circ}
\measuredangle A = \measuredangle B

👉

congruent

is like the geometry version of equal

example

congruent

is like the geometry version of equal

\measuredangle A = 50^{\circ}
\measuredangle B = 50^{\circ}
\measuredangle A = \measuredangle B
\measuredangle A \cong \measuredangle B

👉

congruent

is like the geometry version of equal

example

congruent

is like the geometry version of equal

\measuredangle A = 50^{\circ}
\measuredangle B = 50^{\circ}
\measuredangle A = \measuredangle B
\measuredangle A \cong \measuredangle B

congruent

is like the geometry version of equal

example

congruent

is like the geometry version of equal

\measuredangle A = 50^{\circ}
\measuredangle B = 50^{\circ}
\measuredangle A = \measuredangle B
\measuredangle A \cong \measuredangle B

"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

\overline{AB}=5

👉

congruent

is like the geometry version of equal

example #2

congruent

is like the geometry version of equal

\overline{AB}=5
\overline{PQ}=5

👉

congruent

is like the geometry version of equal

example #2

congruent

is like the geometry version of equal

\overline{AB}=5
\overline{PQ}=5
AB=PQ

👉

congruent

is like the geometry version of equal

example #2

congruent

is like the geometry version of equal

\overline{AB}=5
\overline{PQ}=5
AB=PQ
\overline{AB}\cong\overline{PQ}

👉

congruent

is like the geometry version of equal

example #2

congruent

is like the geometry version of equal

\overline{AB}=5
\overline{PQ}=5
AB=PQ
\overline{AB}\cong\overline{PQ}

congruent

is like the geometry version of equal

example #2

congruent

is like the geometry version of equal

\overline{AB}=5
\overline{PQ}=5
AB=PQ
\overline{AB}\cong\overline{PQ}

"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

\overline{AB}=5
\overline{PQ}=5
AB=PQ
\overline{AB}\cong\overline{PQ}

"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!