Congruence and Similarity

Congruence and Similarity

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Learning Goal:

• To be able to apply the rules of congruence to identify congruent figures

In Geometry, congruent figures are two figures (2D) that have the same shape and size. If two figures are congruent, one of the figures can be rotated, reflected and/or translated (shifted up, down, left and/or right) to match the other figure exactly. 

If triangle DEF (ΔDEF) is congruent to triangle RST (ΔRST), we write ΔDEF ≅ΔRST (triangle DEF is congruent to triangle RST). This is called a congruence statement. 

Corresponding sides and angles refer to the pairs of matching sides or angles that are in the same position in two different shapes. 

Corresponding sides

DE = RS

EF = ST

DF = RT 

Corresponding angles

∠DEF = ∠RST

∠EFD = ∠STR

∠EDF = ∠SRT

Testing for congruence

There are four congruence tests used for triangles. If two triangles satisfy one of the following tests, the two triangles are proved to be congruent. 

SSS: side-side-side

Two triangles are congruent if all corresponding sides are equal. 

SAS: side-angle-side

Two triangles are congruent if two pairs of corresponding sides and the angle included between them is equal. 

ASA: angle-side-angle

Two triangles are congruent if two pairs of corresponding angles and a pair of corresponding sides are equal. 

RHS: right angle-hypotenuse-side

Two right-angled triangles are congruent if the hypotenuses and one pair of corresponding sides are equal.

Multiple Choice

Example

Which congruence test would be used to show that the following pairs of triangles are congruent?

• SSS

• SAS

• ASA

• RHS

Multiple Choice

Example

Which congruence test would be used to show that the following pairs of triangles are congruent?

• SSS

• SAS

• ASA

• RHS

Fill in the Blanks

Find the unknown values of the following congruent pairs of triangles.

Answer: x=___,y=___,z=___ (no spaces, no degree symbol)

Multiple Choice

Example

Using the given information only, which congruence test would be used to show that the following pairs of triangles are congruent?

• SSS

• SAS

• ASA

• RHS

Fill in the Blanks

Find the unknown values of the following congruent pairs of triangles.

Answer: x=___,y=___,z=___ (no spaces, no degree symbol)

Multiple Choice

What does congruent mean?

• Same shape, different size
• Not same shape, or size
• Same size, same shape

Multiple Choice

Which statement is the congruence statement for the 2 triangles?

• ∆EFG $$\equiv$$   ∆MLF

• ∆EFG $$\equiv$$   ∆MFL

• ∆EGF $$\equiv$$  ∆FML

• ∆GEF $$\equiv$$   ∆FML

Multiple Choice

What is ratio of any two corresponding sides?

• Scale Factor
• Corresponding Sides
• Similar Figures

Multiple Choice

What is the scale factor from ABCD to MNOP?

• 2/3

• 3/2

• 2

• 3

Multiple Choice

If the triangles are similar, find x

• 90
• 60
• 30
• 15

Multiple Choice

The triangles are similar by...

• SAS
• AA
• ASA
• SSS