Texas Geometry Staar Diagnostic Exam Hints and Study Guide

7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide

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Draw in a segment connecting points X and Z.

We know that for a triangle to be possible, any side

length must be less than the sum of the other two

sides. Imagine that XY and YZ both were 5 units long,

then XZ would have to be less than 10 units long.

Pg. 334

XZ must be less than what?

A counterexample disproves a conjecture/statement

or makes it false. We need a counterexample where

2 triangles have 2 pairs of sides that are congruent

and a pair of non-included angles that are congruent.Remember non-included means notbetween.

Pg. 242-255

Ex:

Statement: If it is the weekend, then it is Saturday.

Counterexample: Sunday

A deductive argument is an argument made from

rules. You must pick out the valid argument. It will

be helpful to look at the final sentence in eachanswer choice and determine which one is true.

Pg. 88-90

A Are all quadrilaterals parallelograms? Can you

think of some quadrilaterals that are not

parallelograms?

B Do all polygons whose diagonals bisect each other

have opposite sides that are parallel?

C Are all rectangles squares?

D Are all parallelograms quadrilaterals?

For each figure, there is an angle that is inside thecircle but not at the center (central angle) or on the

circle (inscribed angle). Look at the sum of the

intercepted arcs for each figure. What relationship is

there between the measure of an inside angle and

the measure of its intercepted arcs?

Pg. 783

x =

Remember: Dividing by two is the same as

multiplying by

X

Y

Z

z yx C

inside angle

1

2

3

4


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Reflections look like two congruent images side by

side in a mirror.

Rotations look like two congruent images and one of

the images has been turned.

Translations look like two congruent images, but one

of the images has been moved up or down/left orright.

Pg. 824-841

If you divide a 45-45-90 triangle in half it makes 2

45-45-90 triangles. What is the length of the

hypotenuse?

Pg. 356

When you make a horizontal cut, the resulting cross

section is the same shape as the base but smaller.

Pg. 656-657

Square Pyramid Cone

Cross section Cross Section

Label each answer choice front, top, and side. Whichof the figures could not be one of these?

Pg. 661-662

Ex:

45

45

45

45

45

45

45

45

10 ft.

???

5

6

7

8

Top Front Right


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Find the midpoint of segment RG. The equation will

contain this point. Next, find the slope of segment

RG. The perpendicular bisector should have a slope

that is the opposite reciprocal of the slope of RG.

Pg. 182-184

Equations -

Midpoint: (

)

Slope =

(Convert meters to feet first!!)

The shaded region is made up of two shapes: a

trapezoid and a semicircle. The equation for area of

a trapezoid:

The equation for area of a semicircle is half the

equation for the area of a circle:

Pg. 606-607

Draw the quadrilateral. Since segment AB and CD

are parallel but not congruent and A B, yourfigure should look something like this:

Pg. 429

Since one side and one angle are congruent

on the triangles, you need another pair of

congruent sides or angles to prove thetriangles are congruent by one of the

following congruence theorems:

SAS (Side-Angle-Side)

AAS (Angle-Angle-Side)

ASA (Angle-Side-Angle)

SSS (Side-Side-Side)

HL (Hypotenuse-Leg)

Pg. 242-252

SAS AAS ASA

SSS HL

r = ?

h

9

10

11

12

A B

CD


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Which trig. function compares the opposite

side (height of tree) to the adjacent side

(length of trees shadow)?

Pg. 525

Sine of =

Cosine of =

Tangent of =

Some old hippie

What is the similarity ratio for these solids if the

dimensions of the larger solid are double that of the

smaller solid?

Once you find the similarity ratio how do you find the

area ratio and volume ratio?

Pg. 700 (ex 4)

Segment BC will be perpendicular to segment AB

because adjacent sides of a square are perpendicular

(all angles are 90).

Remember: perpendicular lines have slopes that are

opposite reciprocals.

Pg. 184

Mark the diagram with the givens and all the

statements. What things are congruent on

the triangles?Here are the rules to prove triangles are

congruent:





HL (Hypotenuse-Leg)

Pg. 242-252

SAS AAS ASA

SSS HL

50

Opposite

side

Adjacent

side

Similarity

Ratio

Area

Ratio

Volume

Ratio

3

3

13

14

15

16


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Mark the givens on the diagram. You have a side and

an angle that are congruent. If you have another

side, you can use SAS (Side-Angle-Side) as long as the

congruent angles are included or between the

congruent sides.

Pg. 242-252

Ex:

Similar triangles have congruent angles and

corresponding sides that are proportional.

There are 3 ways to prove triangles are

similar:

AA (Angle-Angle)



Pg. 470-473

AA

SSS

SAS

For a triangle to be possible, any side length must be

greater than the sum of the other two sides. If oneside is 15 the sum of the other two sides must be

greater than 15.

Pg. 334

Ex:

To find the probability that a point will be randomlychosen in a certain area, find the area of the region

of success and divide it by the total area.

Pg. 630-633

Side

Angle

Side

Angle

SideSide

17

18

19

20

5 10

3 6

4 8

365

10

A

B

C

8 5

11

8 + 5 > 11


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If mGLK = 55, what is the mJKL? When lines are

parallel, alternate interior angles are congruent.

If mEFJ = 120, what is the measure of the angle

adjacent or right next to it?

Pg. 155-157

Ex:

The equation for circumference of a circle is

2 times pi times the radius (C = 2r). Youare given the circumference; find the radius

by solving backwards (plug in what you

know, to find what you dont know). Once

you find the radius, you should be able tofind the side length of the square fence and

then the perimeter.

The ratio of the side lengths is the same as

the ratio of the perimeters. Find the

perimeter ofABC. What is the ratio ofthe perimeters of the two triangles? Once

you find the ratio of the perimeters, youll

need to set up a proportion to solve for the

shortest side ofDEF.

Pg. 470-473

If the diameter = 10, what is the radius? Theequation for surface area of a cylinder is:

Surface Area (SA) = LA + 2B = 2rh + 2r2

Pg. 681-682

A

B

C

8 5

11

Perimeter = ?

D

E

F

Perimeter = 60

x = ?

21

22

23

24

60

60


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Drop an altitude like its hot, drop it like its

hot, drop it like its hot

Use the Pythagorean theorem to find the

height of the triangle. The area =

Find the missing side of the triangular base

and then add up the sides to get P (the

perimeterof the base). The equation for

surface area of a prism is:

Surface Area (SA) = LA + 2B = Ph + 2B

B = area of the base (remember: the base is a

triangle!)

h (height) = distance between the bases

Pg. 681-682

Use the equation for area of a circle (A = r2) to findthe radius by solving backwards (plug in what you

know, to find what you dont know). The perimeter

of the sector (pie slice) has two sides that are radii.

To find the arc length use this equation:

Arc Length = ( 3) [x = the central angle]

Pg. 764-766

There are 2 similar triangles formed by the

intersecting roads -- a big and a little one.

Pg. 470-473

36

18

?

18

36

36

radius

radius

arc length

1st

St 2nd

St 3rd

StKyle St 500 ft 375 ft

375 ft.x ft.

875 ft.(x +650)

375 ft500 ft

25

26

27

28


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The longest side of the triangle is across from the

largest angle and the shortest side is across from the

smallest angle.

Pg. 333

Do supplementary angles always form a

linear pair?

Angles 1 & 2 are both 90 and aresupplementary but they are not a linear pair.

If angles 1 & 2 are supplementary, does it

mean they are congruent?

The equation for volume is:

V = Bh (B = area of the base)

Make the 8 x 12 rectangle your base. Find the

volume of the original flower box, and then find the

volume using the new length of 24 inches.

Pg. 697-698

Find the difference in the number of dots in each

figure. How much does it go up by from the first

figure to the second figure? From the second figure

to the third figure?

Pg. 74-77

1

2

1 5 11

+4 +6

?

+?

29

30

31

32


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The equation of a line can be written in

slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

Perpendicular lines have slopes that areopposite reciprocals. The slope of line m is 7.

What will the slope of line n be? To find the

y-intercept plug in the x and y values of the

point provided and solve for b. (Pg. 184)

The house and garage together have a length of 13.5

inches in the outline. 1.5 inches = 14 ft.

DBR is an inscribed angle. An inscribed angle is half

the intercepted arc. What is the measure of arc DR?

mDAR is a central angle. A central angle and the

intercepted arc have the same measure.

Pg. 772-773

z = or y = 2z

The key to this problem is drawing a correct

diagram and then using the Pythagorean

theorem to find the sides of the rhombus.

12

5

5

12

?

33

34

35 y

z

5

12

36


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The midsegment of a trapezoid is equal to the sum of

the bases, divided by 2. The bases are segments RA

and TP.

Pg. 431

The intersection forms a 45-45-90 triangle.

Pg. 356-358

Ex: To go from leg to hypotenuse multiply by .

Since a tessellation is a tiling of shapes with no gaps,

the angles where the tiles meet add up to 360.

Pg. 863-864

Things to remember about tessellations:

- Triangles, quadrilaterals, and regularhexagons always tessellate

- The sum of the angles at any vertex is 360

To write a contrapositive statement you must flip

and negate the hypothesis and conclusion of the

original conditional statement.

Pg. 81-83

Converse flip the hypothesis and conclusion

Inverse negate the hypothesis and conclusion

Contrapositive flip and negate the hypothesis and

conclusion

x

45

x

45

Hypotenuse

Legs 45

2

Multiply

by

45

37

38

39

40


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2 planes perpendicular to the same line are parallel.

The triangle is isosceles if the distance between

points A & C and points B & C are equal.

Use the distance formula:

Pg. 43-44

A(-1,0) and B(4,-3)

Use the distance formula:

Pg. 43-44

First, find one interior angle of the regular

hexagon. To do this, youll need to find thesum of the interior angles and divide by the

number of angles.

Sum of interior angles = (n - 2)180

Once you find the interior angle of the

hexagon, you can solve for x.

Pg. 382-385

x

y

B(5, 6)

C (x, y)

A (4, 5)

41

42

43

44


12/14

Volume of a rectangular prism:

V = Bh (B is area of the base)

Since the base is a rectangle, B = Length x

Width.

ThereforeVolume = length x width x height

If the tank is full, you will have the

volume. Multiply your volume byto get

the volume of the tank when it isfull.

The truck bed forms a 30-60-90 triangle.

Pg. 356-358

Ex: Hypotenuse to short leg

Solve for a by using the Pythagorean theorem. The

side lengths must be some multiple of a Pythagoreantriple. Find the greatest common factor of each side,

and then divide each side by it to find what

Pythagorean triple is related.

Pg. 348-350

Common Pythagorean Triples

Triples Multiples3-4-5 6-8-10, 9-12-15, 12-16-20, 15-20-255-12-13 10-24-26, 15, 36, 397-24-25 14-48-50, 21, 72, 758-15-17 16-30-34, 24-45-519-40-41 18-80-82, 27-120-123

Properties of Rectangles:

-Opposite sides are parallel and congruent-Diagonals bisect each other

-Diagonals are congruent

-Angles are 90

Pg. 418-420

2x

60

x

30

Short leg

HypotenuseLong leg

40

60

20

30

Divide

by 2

45

46

47

48


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There are 3 ways to prove triangles are

similar:

AA (Angle-Angle)



Which one of the answer choices has 2 sidesthat are proportional and an included angle

that is congruent to the originals triangle?

Pg. 470-473

The 35 angle is an angle of elevation.

Pg. 544-546

Sine of =

Cosine of =

Tangent of =

Some old hippie

The equation for surface area of a prism is:

Surface Area (SA) = Ph + 2B

Choose the bottom rectangle (2 x 1.5) to be

your base. What is P (the perimeter of the

base)? What is B (the area of your base)?

Pg. 681-682

Here are the rules to prove triangles are

congruent:





HL (Hypotenuse-Leg)

Pg. 242-252

SAS AAS ASA

SSS HL

35

Opposite side

(height)

Hypotenuse

(rope)

49

50

51

52


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Texas Geometry Staar Diagnostic Exam Hints and Study Guide

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