Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
100
A, B, and C are collinear points. AB is four times greater than BC. If AC is 120, find the length of AB.
AB= 96
100
If point B is between A and C, and AB = 5x - 2, BC = 3x + 6, and AC = 38, find x, AB, and BC.
x = 4.25
AB = 19.25
BC = 18.75
100
How does y= (x - 2)2 transform y= x2
The (x - 2) means a horizontal shift of 2 units to the right
100
Two triangles have three pairs of congruent sides, Which condition proves they are congruent?
SSS (Side-side-side)
100
A right triangle has an angle where the opposite side is 3 and the adjacent side is 4. Find tan and sin.
tan= 3/4
sin= 3/5
200
m<WXZ = 140o , find each measure.
x=9
m<WXY= 88o
m<YXZ= 52o
200
If ∠ABD = 4x + 5 and ∠DBC = 2x - 1, and ∠ABC = 80°, find x and the angle measures.
x ≈ 12.67°
m∠ABD ≈ 55.68°
m∠DBC ≈ 24.34°
200
How does y= -3f(x) transform y= f(x)?
The -3 causes a vertical stretch by a factor of 3 and a reflection across the x-axis
200
Given ABC and DEF, if AB=DE, BC=EF, and <B= <E, are the triangles congruent?
Yes, by SAS
200
From 40m away, the angle of elevation to a building's top is 32o. Find the building's height.
tan= 25m
300
m<SRT = 55o, m<TRQ = 164o, find m<QRS
109o
300
Ray YW bisects ∠XYZ. If m∠XYW = 5x - 4 and m∠WYZ = 3x + 10, find x and m∠XYZ.
x = 7
m∠XYZ = 62o
300
Reflect shape C in the line y= 1
Trace the shape, flip it over the line y= 1, keeping the same distance from the line, and then draw the new points
300
If <P= <S, <Q= <T, and PQ= ST, are PQR and STU congruent?
Yes, by ASA
300
A triangle has sides a=7, b=8 and angle C= 30o. Find side c using the Cosine Rule.
c2=72+82−2(7)(8)cos(30∘)=49+64−112(3/2)=113−563c squared equals 7 squared plus 8 squared minus 2 open paren 7 close paren open paren 8 close paren cosine open paren 30 raised to the composed with power close paren equals 49 plus 64 minus 112 open paren the square root of 3 end-root / 2 close paren equals 113 minus 56 the square root of 3 end-root
.
c=113−563c equals the square root of 113 minus 56 the square root of 3 end-root end-root
.
400
m<KLM = 46o, m<NLM = 28o, find m<KLN
74o
400
∠A and ∠B are complementary. If m∠A = 2x + 15 and m∠B = x - 5, find x and the measures.
x ≈ 26.67°
m∠A ≈ 68.34°
m∠B ≈ 21.67o
400
Translate the shape D by the vector (-2, 3)
Move every point of shape D two units left and three units up
400
In XYZ and QRS, XY=QR, YZ=RS, and XZ=QS. Prove they are congruent.
Third space learning uses SAS, but SSS is also applicable.
XY= QR
YZ= RS
XZ= QS
400
What is cos(60p)?
1.2
500
If m<ABC = (17x + 8)o, m<ABD = 42o, and m<CBD = (12x - 4)o, find each measure.
x=6
m<ABC = 110o
m<CBD = 68o
500
Lines l || m, t is a transversal. If m∠3 = 5x - 2 and m∠6 = 3x + 10 (same-side interior), find x and the angles.
x = 21.5
m∠3 = 105.5o
m∠6 = 74.5o
500
Reflect over A (2,2), B (4,4), and C (5,1) to the y-axis
A'= (-22)
B'= (-4,4)
C'= (-5,1)
500
In a diagram with overlapping triangles, you find AB= BC, AD=CD, and BD is common. Prove ABD≅CBD.
SSS (AB=BC, AD=CD, BD=BD)
Congruent angles (<ABD=<CBD), and then ABE≅CBE by SAS
500
b=5
or
b= square root 25