BPW - Intro to Congruency

Intro to Congruency

How do transformations help to determine if two shapes are congruent?

Transformations are:

• Rotations: "turning" a shape a certain number of degrees

• Reflections: "flipping" a shape over a line of reflection

• Translations: "sliding" a shape a certain distance in a certain direction

Multiple Choice

A slide is also called a _________.

• Translation

• Reflection

• Rotation

Multiple Choice

A turn is also called a ___________.

• Translation

• Reflection

• Rotation

Multiple Choice

A flip is also called a _________.

• Translation

• Reflection

• Rotation

Multiple Choice

Translations, reflections and rotations are all known as ________________________.

• Geometry
• Transformations
• Congruent

Transformations are also called "rigid motions" because they do not change the object's size or shape - it just moves to a new location!

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Congruency

Two shapes are CONGRUENT if one can be "mapped" (matched up EXACTLY by moving it) onto the other shape using only rigid motions (transformations).

Congruent? YES!

The orange shape could rotate/turn and then translate/slide onto the blue one.

Congruent? NO!

The blue triangle is larger than the red triangle. They would not match up exactly.

Congruent? YES!

The shape on the left could reflect/flip and then translate/slide onto the right one.

Multiple Choice

Are these two shapes congruent or not congruent?

• congruent
• not congruent

Multiple Choice

Are these shapes congruent or not congruent?

• congruent
• not congruent

Multiple Choice

Are these two shapes congruent or not congruent?

• congruent
• not congruent

Multiple Choice

Are these shapes congruent?

• Yes
• No

When shapes are congruent, we identify the points, lines or angles that CORRESPOND to each other from the two shapes.

Who corresponds to who?

Here are a few...

• Vertex A corresponds to Vertex E

• Side BC corresponds to Side DF

• Angle C corresponds to Angle F

Multiple Choice

Angle A corresponds to which angle?

• ∠B

• ∠E

• ∠D

• ∠F

Multiple Choice

Which side corresponds to side DF?

• AB

• AC

• BC

• ED

Multiple Choice

Tell whether the two figures are congruent.

• Yes, same size and same shape
• No, same shape but different sizes
• No, different size and different shapes

Multiple Choice

If LMNO is congruent to WZYX, Which angle is congruent to ∠O?

• ∠Z

• ∠X

• ∠Y

• ∠W

Multiple Choice

If Δ ABC is congruent to Δ DEF , which side corresponds to AC?

• EF

• DF

• BE

Multiple Choice

If Δ ABC is congruent to Δ DEF , which angle is congruent to angle B?

• ∠E

• ∠D

• ∠C

• ∠F