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Flashcards: Congruence and similarity criteria for triangles

Two of the angles of a triangle are congruent; the third has measure ten degrees greater than either one of the first two. What is the measure of the third angle?

$66 \frac{2}{3} ^{\circ }$

$73\frac{1}{3}^{\circ }$

$63 \frac{1}{3} ^{\circ }$

$56 \frac{2}{3} ^{\circ }$

$53 \frac{1}{3} ^{\circ }$

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Flashcards: Congruence and similarity criteria for triangles

Two of the angles of a triangle are congruent; the third has measure ten degrees greater than either one of the first two. What is the measure of the third angle?

Your answer:

$73\frac{1}{3}^{\circ }$

Your answer:

$63 \frac{1}{3} ^{\circ }$

Your answer:

$56 \frac{2}{3} ^{\circ }$

Your answer:

$53 \frac{1}{3} ^{\circ }$

Correct answer:

$66 \frac{2}{3} ^{\circ }$

Explanation:

Let be the measure of the third angle. Since its measure is ten degrees greater than either of the others, then the common measure of the other two is x- 10 . The sum of the measures of the angles of a triangle is 180 degrees, so

x+ (x-10) + (x-10) = 180

To solve for , first ungroup and collect like terms:

x+ x - 10 + x - 10 = 180

x+ x + x - 10 - 10 = 180

3x - 20 = 180

Isolate ; first add 20:

3x-20+20 = 180 + 20

3x= 200

Divide by 3:

$3x \div 3 = 200 \div 3$

Since $200 \div 3 = 66 \textup{ R }2$ ,

$x = 66 \frac{2}{3}$ .

The third angle measures $66 \frac{2}{3} ^{\circ }$ .

Flashcards: Congruence and similarity criteria for triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\angle C \cong \angle F$ and $\angle A \cong \angle D$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be proved by the AA Similarity Postulate.

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be prove by the Isosceles Triangle Theorem.

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be prove by the SSS Similarity Theorem.

Insufficient information exists to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be proved by the SAS Similarity Theorem.

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Flashcards: Congruence and similarity criteria for triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ such that $\angle C \cong \angle F$ and $\angle A \cong \angle D$ .

Does sufficient information exist to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ , and if so, by what postulate or theorem?

Your answer:

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be prove by the Isosceles Triangle Theorem.

Your answer:

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be prove by the SSS Similarity Theorem.

Your answer:

Insufficient information exists to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

Your answer:

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be proved by the SAS Similarity Theorem.

Correct answer:

$\bigtriangleup ABC \sim \bigtriangleup DEF$ can be proved by the AA Similarity Postulate.

Explanation:

We are given that, between the triangles, two pairs of corresponding angles are congruent. By the AA Similarity Postulate, this is enough to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

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Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

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Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

Flashcards: Congruence and similarity criteria for triangles

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