Consider the diagram.

a

Why is $BE$`B``E` parallel to $CD$`C``D`?

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of equal corresponding angles.

A

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of supplementary cointerior angles.

B

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of equal alternate angles.

C

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of equal corresponding angles.

A

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of supplementary cointerior angles.

B

$\angle ABE$∠`A``B``E` and $\angle ACD$∠`A``C``D` form a pair of equal alternate angles.

C

b

Which angle is equal to $\angle BEA$∠`B``E``A`?

$\angle BEA=\editable{}$∠`B``E``A`=

c

How do we know that $\triangle ABE\simeq\triangle ACD$△`A``B``E`⫻△`A``C``D`?

Two right-angled triangles have the ratio of their hypotenuses equal to the ratio of another pair of matching sides

A

Two pairs of matching sides are in the same ratio and the included angles are equal

B

All pairs of matching sides are in the same ratio

C

All three pairs of corresponding angles are equal.

D

Two right-angled triangles have the ratio of their hypotenuses equal to the ratio of another pair of matching sides

A

Two pairs of matching sides are in the same ratio and the included angles are equal

B

All pairs of matching sides are in the same ratio

C

All three pairs of corresponding angles are equal.

D

d

What is the scale factor relating $\triangle ABE$△`A``B``E` to $\triangle ACD$△`A``C``D`?

e

Solve for the value of $f$`f`.

Easy

Approx 4 minutes

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calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar