Answers Fall 24 GMS Geometry Concepts and Connections BSolving for Angle Measures of Right Triangles

Central Angles Answers

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Quadrilateral JKLM was dilated according to the ruleDO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.

(0, -4)

(0, -1)

(0, 0)

(0, 4)

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Which best explains why all equilateral triangles are similar?

All equilateral triangles can be mapped onto each other using dilations.

All equilateral triangles can be mapped onto each other using rigid transformations.

All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.

All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of R T is x.

12 units

15 units

20 units

25 units

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle? Round to the nearest tenth.Area of a triangle = bh

68.7 cm2

161.8 cm2

381.3 cm2

450.0 cm2

Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters.

m∠V = 30°, m∠U = 60°, m∠W = 90°

m∠V = 90°, m∠U = 60°, m∠W = 30°

m∠V = 30°, m∠U = 90°, m∠W = 60°

m∠V = 60°, m∠U = 90°, m∠W = 30°

On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units.

Yes, because corresponding sides are parallel and have lengths in the ratio

Yes, because both figures are rectangles and all rectangles are similar.

No, because the center of dilation is not at (0, 0).

No, because corresponding sides have different slopes.

The hypotenuse of a 45°-45°-90° triangle measures units.

11 units

units

22 units

units

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

∠DFE is 4 times greater than ∠GFH.

∠FHG is the measure of ∠FED.

∠DFE is congruent to ∠GFH.

∠FHG is congruent to ∠EFD.

The equation can be used to find the measure of angle LKJ.

41°

45°

49°

55°

Triangles A B C and A double-prime B double-prime C double-prime connect at point C. Triangle A B C is rotated and then made smaller to form triangle A double-prime B double-prime C double-prime.

a rotation and a reflection

a translation and a dilation

a reflection and a dilation

a dilation and a rotation

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.

units

units

Which equation can be used to find the length of ?

(10)sin(40o) = AC

(10)cos(40o) = AC

= AC

Consider △RST and △RYX.

StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction

StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction

StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction

StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction

In which triangle is the value of x equal to tan−1? (Images may not be drawn to scale.)

A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle between the 2 sides is x.

A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle opposite to side with length 3.1 is x.

A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 5.2 is x.

A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 3.1 is x.

Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6.

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction

StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U

StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction

Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.

because both triangles appear to be equilateral

because∠MNL and ∠ONP are congruent angles

because one pair of congruent corresponding angles is sufficient to determine similar triangles

because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm.

34.8°

39.4°

50.6°

55.2°

Triangle ABC is a right triangle and cos(22.6o)=. Solve for b and round to the nearest whole number.

tan(22.6o) =

Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x.

sin(x) =

cos(x) =

The diagonal of rectangle ABCD measures 2 inches in length.

1 inch

inches

4 inches

inches

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