Geometry Ch. 4

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Which statement regarding the diagram is true?

XX m∠JKM + m∠MLK = 180°

Which statements are always true regarding the diagram? Check all that apply.

m∠5 + m∠3 = m∠1 m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS?


What is the value of x?


The value of x is (130, 134)

XX 86

The value of x is (9x, 5x, 9+x)


Which is a true statement about the diagram?

m∠1 + m∠2 = 180°

Which statement about the value of x is true?

x > 38

Which statement regarding the interior and exterior angles of a triangle is true?

An exterior angle is supplementary to the adjacent interior angle.

What is the value of x? (35, 58)

x = 93

Fiona’s school has three hallways that make up three sides of a triangular building design. In the morning, Fiona walks 90 yards through the first hallway to get to the next. In the afternoon, she walks 60 yards through a second hallway to exit the building.

What are the possible lengths of the third hallway that she did not walk through?

between 30 yards and 150 yards

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

m∠X + m∠Y < 90°

If triangle DEF has a 90° angle at vertex E, which statements are true? Check all that apply.

The angle at vertex D is acute. Triangle DEF is a right triangle.

Which statements about the diagram are true? Check all that apply. (DFE 4,9)

a, c, e

The value of x must be greater than (12, 15)


Which are the possible side lengths of a triangle?

4 cm, 8 cm, 10 cm

The isosceles triangle has a base that measures 14 units.

The value of y, the length of each leg, must be

greater than 7

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

XX try c Iliana will be able to construct a triangle because the sum of any two sides is less than the third side.

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

4x < h < 10x

Triangle QRS has the angle measures shown.

m∠Q = (1x)°
m∠R = (3x)°
m∠S = (6x)°

The measure of the obtuse angle equals


to make a triangle:

Consider the triangle.

Which shows the order of the angles from smallest to largest?

angle B, angle A, angle C

Lee is creating a garden with the dimensions shown.

He creates paths through the garden along AB, XY, YZ and . Which correctly compares the lengths of the paths?


Consider the triangles shown.

If mUTV &lt; mUTS &lt; mSTR, which statement is true?

A: VU < US < SR by the hinge theorem.

Which statement is true regarding triangle TUV?

Angle V is the smallest angle.

In the triangles, QR = DE and SR = FE.

Which statement about the sides is true?


Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the library. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle.

The largest angle made during his trip is at

the mall

Triangle XYZ is shown, where n ≥ 5.

Which statements are true regarding the sides and angles of the triangle? Check all that apply.

XX a,c,e

Based on the given angle measures, which triangle has side length measures that could be correct?


Complete the statement.

Since angle B is the largest angle,________ is the side


Consider the triangle.

Which statement is true about the lengths of the sides?

The three sides have the same length.

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

What is RS?

7 feet

In triangle DEF, CG = (x + 5) units and DG = (3x – 2).

What is DG?


In triangle ABC, EG = x inches and BG = (5x – 12) inches.

What is EB


ABC is an obtuse triangle. Which is true about point D?

Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.

In the diagram, GB = 2x + 3..

What is GB?


A centroid is the intersection of three

medians in a triangle.

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units.

What is AF?

51 units

In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

What is NS?

20 cm

An orthocenter is the intersection of three

altitudes in a triangle.

In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK?

Point G cannot be a centroid because JG is shorter than GE.

Which is the only center point that lies on the edge of a triangle?

the circumcenter of a right triangle

The figure shows a circle inscribed in a triangle.

To construct the inscribed circle, angle bisectors were first constructed at each angle of the triangle. Which happened next?

XX A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.

Point Y is the circumcenter of ΔDEF.
Find the length of FY.
FY measures ____ units


What value of n would make point A the circumcenter?


In the diagram, Z is the circumcenter of triangle TUV.

What is the length of VZ?

10 units

Point A is the point of concurrency of the angle bisectors of ΔDEF.
What is the length of ZA?

ZA = 3cm

Point O is the incenter of triangle ABC.
What is mQOB?


Point X is the circumcenter of ΔABC.

What is the length of MB?

2.5 cm

Point P is the incenter of ΔRST.
Which must be true?


Point Y is the circumcenter of triangle DEF.
Which statement is true about point Y?

Point Y is the center of the circle that passes through points D, E, and F.

Which new angle is created by extending one side of a triangle?

an exterior angle

Triangle DEF is isosceles, where . Angle D is bisected by segment DG, creating angle GDE with a measure of 29°.

What is the measure of angle DFE?


In triangle ABC, BG = 24 mm. What is the length of segment GE?


Consider the triangle.
The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle?

b: mA = 32°, mB = 53°, mC = 95°

In the diagram, which must be true for point P to be the centroid of the triangle?

JM = ML, LO = OK, and KN = NJ.

In the triangles, HG = MP and GK = PN.

Which statement about the sides and angles is true?

a: mG > mP

In the triangles, BC=RS and AC=TS.

If RT is greater than BA, which correctly compares angles C and S

b: mC < mS

Which type of triangle will always have a perpendicular bisector that is also an angle bisector?


ZE is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .

Which must be true?

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?


Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side at point M.

What is the length of MC?

16 mm

Point Z is the circumcenter of ΔTUV.

What is mZUB?


In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?

3 < QS < 13

Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown.

What should Jace do first to find the exact location of the center of the circular water bowl?

He should bisect each of the angles at the vertices of the triangular table top

Which diagram shows possible angle measures of a triangle?


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