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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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:
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
50
Opposite
side
Adjacent
side
Similarity
Ratio
Area
Ratio
Volume
Ratio
3
3
13
14
15
16
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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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
7/30/2019 Texas Geometry Staar Diagnostic Exam Hints and Study Guide
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There are 3 ways to prove triangles are
similar:
AA (Angle-Angle)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
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:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
AAS (Angle-Angle-Side)
ASA (Angle-Side-Angle)
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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