CONGRUENCE VS. EQUALITY

​CONGRUENCE VS. EQUALITY

By Raymee Burrell

Give all the names of the figures below.

Pre Instructional Activity: Notation Review

Multiple Choice

Pre Instructional Activity: Notation Review

Name the figure.

• $$\overline{RT}$$

• $$\overleftarrow{R}\overrightarrow{T}$$

• $$\overrightarrow{RT}$$

Multiple Choice

Pre Instructional Activity: Notation Review

Name the figure.

• $$\overline{PQ}$$

• $$\overleftarrow{P}\overrightarrow{Q}$$

• $$\overrightarrow{PQ}$$

Multiple Choice

Pre Instructional Activity: Notation Review

Name the figure.

• $$\overline{LM}$$

• $$\overleftarrow{L}\overrightarrow{M}$$

• $$\overrightarrow{LM}$$

• $$\overrightarrow{ML}$$

Multiple Select

Pre Instructional Activity: Notation Review

Name the figure.

Select all that apply.

Hint: use any 3 points that do not form a line

• Plane P

• Plane ABC

• Plane BCD

• Plane ACD

• Plane ABD

​🟣Students will distinguish between congruence and equality and correctly use notation to describe geometric relationships.

​​🎯Learning Target

​🟢Define congruence and equality in the context of geometry.

🟢Explain the difference between congruent figures and equal measurements.
🟢Use correct notation:






🟢Identify errors in notation and correct them.
🟢Justify why two figures are congruent or why two measurements are equal using geometric reasoning

​​✅Success Criteria

​​Students are learning

​​Students are successful when

​➖Use ≅ to show congruence between figures (e.g., triangles, segments, angles).
➖Use = to show equality between numerical values (e.g., lengths, angle measures).

SYMBOLS USED IN GEOMETRY

Match

Match the symbols to their meaning

Equal

Congruent

Similar

• Equal

• Congruent

• Similar

Match

Match the symbols to their meaning

Parallel

Triangle

Angle

Perpendicular

• Parallel

• Triangle

• Angle

• Perpendicular

SYMBOLS USED IN GEOMETRY

Match

Match the symbols to their meaning

feathers

corner box

hash marks

arcs

• feathers

• corner box

• hash marks

• arcs

Draw

Sketch, label, and use markings.

$$\overline{JK}\ \parallel\ \overrightarrow{MR}$$

Draw

Sketch, label, and use markings.

$$\angle EFG\ \cong\ \angle GFH$$

Labelling

Fill in the blank with the following words:

actual

measure

notation

symbols

Drag labels to their correct position on the image

actual

measure

notation

symbols

Multiple Choice

CONGRUENCE describes figures having _____ length or measure

• equal

• never

Multiple Choice

EQUALITY _______assume figures are drawn to scale.

• equal

• never

Multiple Choice

CONGRUENCE

Figures are ________.

$$\overline{AB}\ \cong\ \overline{CD}$$

$$∠ABC\ ≅\ ∠DEF$$

$$ΔABC\ ≅\ ΔDEF$$

• congruent (≅)

  
  

• equal (=)

Multiple Choice

EQUALITY

Measures are ________.

AB = CD

m∠ABC = m∠DEF

• congruent (≅)

  
  

• equal (=)

Multiple Choice

CONGRUENCE

$$\overline{AB}$$ is a ____________.

  The bar over the letters refers to the actual segment.

Read aloud, “segment AB”

• figure (segment)

• measure (length)

Multiple Choice

EQUALITY

AB is a ____________.

The letters without the bar refer to the segment length.

Read aloud, “the length of segment AB”

• figure (segment)

  
  

• measure (length)

Multiple Choice

CONGRUENCE

$$\angle ABC$$ is a ____________.

  ∠ refers to the actual angle

read aloud, “angle ABC”

• figure (angle)

• measure (of an angle)

Multiple Choice

EQUALITY

$$m∠ABC$$ is a ____________.

m∠ refers to the numerical measure of the angle

read aloud, “measure of angle ABC”

• figure (angle)

  
  

• measure (of an angle)

Categorize

Options (11)

$$\overline{RS}=\overline{QT}$$  

$$m∠RST\ ≅\ m∠ABC$$  

$$∠MNO\ ≅\ ∠FDC$$  

$$ΔWXY\ =\ ΔJKL$$  

$$ΔWXY\congΔJKL$$  

$$m∠1\ ≅m∠5$$  

$$∠1\ ≅∠5$$  

$$m∠1=m∠5$$  

$$∠MNO=∠FDC$$  

$$∠RST\ ≅\ ∠ABC$$  

$$\overline{RS}\cong\overline{QT}$$  

Determine whether each statement is acceptable or not.

Acceptable

Not Acceptable

Draw

TOD:

Mark the sketch with the given information.

m∠ABC = 90°

AB ≅ CB 

∠BAC ≅ ∠BCA

Poll

SELF ASSESSMENT

Select One