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Academic Geometry
Unit 3 Reasoning
Name
Date
Complete the chart with a value in the first column and a theorem, relationship, or vocabulary word
justification in the second column.
m<BCD = 42
m<DCF = 138
m<ABD = 90
m<ADB = 68
m<EDC = 64
m<ADC = 116
∆ Sum( ∆BCD)
Linear Pr to <BCD
Linear Pr to <CBD
∆ Sum (∆ADB)
m<SCT = 90
m<PCU = 49
m<QCR = 41
m<PCR = 131
m<QCT = 180
vertical < to <PCQ
Complementary < to <UCT
Vertical < to <UCT
Adjacent angles (< addition)
Straight <
Adjacent < (< addition)
m<JEX = 36
∆ sum
m<TXE = 91
Ext < of ∆ (linear pr)
m<HJE = 90
Right angle
m<JXH = 91
Vertical <s (linear pr)
m<JHX = 54
∆ sum
__HX__ is the shortest side of ∆HJX.
__JX___ is the largest side of ∆JEX.
m<DWK = 20
∆ sum
m<DXK = 51
Linear pr (ext < of ∆)
m<DKX = 70
∆ sum
m<WDK = 90
Adjacent < (< addition)
∆WDK is a _right_ _scalene_ triangle.
__DX__ is the shortest side of ∆WDX.
Given AB=BC=CD=DE, <JBD=<BDF=108
m<ABJ = 72
Linear pr
m<CBD = 72
Linear pr (vertical <s)
m<BDC = 72
Linear pr
m<BCD = 36
∆ sum
∆CBD is a _acute_ _isosceles_ triangle.
Draw AC
∆ACB is
Isosceles obtuse ∆
m<PAN = 18
Linear pr
m<PNA = 31
Linear pr
m<APN = 149
∆ sum
∆ANP is a _obtuse__ _scalene_ triangle.
m<IDK = 14
Linear pr
m<DKI = 106
∆ sum
Side _IK__ < Side _DK__ < Side _IK__
∆IDK is a _obtuse_ _scalene_ triangle.
m<ABC = 96
Ext < of ∆
m<BAC = 43
Linear pr (∆ sum)
Side _AB_ < Side _BC_ < Side _AC_
∆ABC is a _obtuse_ _scalene_ triangle.
State the order of the sides and angles for each triangle below:
<S , <R, <Q
RQ < SQ < RS
<H, <M, <P
MP < HP < HM
<P, <Q, <I
IQ < PI < PQ