Triangle Congruence Challenge Quiz: Advanced Proofs & Apps

Question 1

In $	riangle ABC$, $D$ is the midpoint of $\overline{AB}$ and $E$ is the midpoint of $\overline{AC}$. A student wants to prove $	riangle ADE \cong 	riangle CDA$.

Which statement is **most** needed to make a correct congruence proof possible?

Accepted Answer

$\overline{DE} \parallel \overline{BC}$

Answer

$\overline{AB} \cong \overline{AC}$

Answer

$\angle AED \cong \angle CDA$

Answer

$\angle DAE \cong \angle CAD$

Question 2

In $	riangle ABC$, point $D$ lies on $\overline{BC}$ such that $BD \cong DC$. If $AD$ bisects $\angle BAC$, which statement must be true?

Accepted Answer

$AB \cong AC$

Answer

$\angle ABC \cong \angle ACB$ only if $AD$ is an altitude

Answer

$AD \perp BC$

Answer

$BD:DC = AB:AC$ but $AB$ and $AC$ may differ

Question 3

In $	riangle ABC$, points $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$ satisfy $DE \parallel BC$. Given $AD = 6$, $DB = 4$, and $AE = 9$, find $EC$.

(Use congruence/similarity reasoning created by parallel lines.)

Accepted Answer

$EC=6$

Answer

$EC=9$

Answer

$EC=15$

Answer

$EC=3$

Triangle Congruence Challenge Quiz: Advanced Proofs & Apps

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