10M2T1: Similarity

Triangle QRS has a perimeter of 55. If segment RT bisects angle R, what is the length of segment QT ?

• 10

• 12

• 15

• 18

Tags

CCSS.HSG.CO.C.9

Victoria holds a 5-foot long fishing pole. The fishing line extends 3 feet to the water’s surface and then another 12.6 feet to a hook. How far is the fish from the hook?

• 21 ft

• 24.6 ft

• 27 ft

• 30.6 ft

Tags

CCSS.8.G.B.8

• 11

• 14

• 15.6

• 16.2

Tags

CCSS.HSG.CO.C.9

• Angle Bisector Theorem

• Alternate Interior Angle Theorem

• Triangle Sum Theorem

• Angle-Angle Similarity Theorem

Tags

CCSS.HSG.SRT.A.2

Altitude NP is drawn in triangle MNO. Which of the following can prove that NP is the geometric mean between MP and PO?

• Right angles MPN, NPO, and ONM are congruent. Triangles NMO and NMP share ∠NMP, and triangles NMO and NOP share ∠NOP. So, triangles NMO, NMP, and NOP are similar by the AA Similarity Theorem So, MP/NP =NP/OP.

• Since right angles are congruent, ∠MPN, ∠NPO, and ∠ONM are congruent. Segment NP bisects angle ∠MNO, so ∠MNO is congruent to ∠ONP. So, triangles NPM and ONP are similar, and MP/NP = NP/OP.

• Segment NP bisects angle ∠MNO, so ∠MNP = 1/2∠MNO and ∠ONP= 1/2∠ONM. By substitution, MP/NP = NP/OP.

• By the Alternate Interior Angle theorem, ∠MNP = 1/2∠NPO and ∠ONP =1/2∠NPM. By substitution, MP/NP = NP/OP.

Tags

CCSS.HSG.CO.C.9

A 30-foot-long support wire for a 16-foot high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the street light is 6 feet. How tall is the building?

• 16 feet

• 20 feet

• 32 feet

• 48 feet

Tags

CCSS.8.G.B.8

What theorem could be used to show triangles ABC and DEF are similar?

• Side-Side-Side Similarity Theorem

• Side-Angle-Side Similarity Theorem

• Angle-Angle Similarity Theorem

• Side-Side Similarity Theorem

Tags

CCSS.HSG.SRT.B.5

A super-heroine slides down a 25-yard-long wire from the top of a 20-yard-tall building into a window 2 yards below the top of a 12-yard-tall building. Her photo is taken by a photographer when she is at point A. At that moment, how far is she from the window?

• 4 yds

• 5 yds

• 6 yds

• 20 yds

Tags

CCSS.8.G.B.8

In triangles TUW and WXT, ∠U and ∠X are congruent. Andre wants to prove that these triangles are similar. Which of the following is a counterexample to show that triangles TUW and WXT are NOT similar?

• ∠U ≅ ∠X, but ∠UTW is not congruent to ∠XWT

• ∠U ≅ ∠X, but ∠UWT ≅ ∠XTW and ∠UTW ≅ ∠XWT.

• ∠U ≅ ∠X, but ∠UWT ≅ ∠UTW and ∠XTW ≅ ∠XWT

• ∠UWT ≅ ∠UTW, ∠XTW ≅ ∠XWT, but ∠U is not congruent to ∠X.

Tags

CCSS.HSG.SRT.A.2

Triangles ABC, ABD, and BCD are similar right triangles. Yoshi writes that AD/BD = BD/CD and AD/AB = AB/AC. What additional statement can Yoshi use to complete a proof that BD² + AB² = AD² ?

• AB + BD = AC + CB + CD

• AD = AC/CD

• AB/BD = AC/CD

• AD = AC + CD

Tags

CCSS.8.G.B.8