Congruence and Constructions - Part 1ongruence and Constructions - Part 1
Alison should do for her first step :
Place the point of the compass on point M and draw an arc using width for the opening of the compass that is greater than ½ MN
1.Points P is on the perpendicular
Bisector of ABGiven
2.AX≅ BXDefinition of bisector
3. ∠PXA and ∠PXB are right anglesDefinition of perpendicular
4.ASA Congruence PostulateAll right angles are congruent
5.PX≅PXReflexive property of congruence
6.△AXP ≅△BXPSAS Congruency Postulate
7.PA≅ PBCorresponding parts of
congruent triangles are
XXXXXXXXX
8.XXXXX X XX XXXXXXXXXXXX XXXXXXXXXXXXXX of XXXXXXXXXXXX
XXXXXXXXX XX XX
1.KM XX XXX XXXXXXXX XX∠XXXXXXXX
X.∠XXX =∠LKMXXXXXXXXXX XX bisector
X.∠XXX and ∠KYM are right anglesGiven
4. ∠XXX≅ ∠XXX All XXXXX XXXXXX are congruent
X.MK = MK Reflexive Property of
XXXXXXXXXX
X. △XXX ≅△KYM XXX XXXXXXXXXX XXXXXXXXX
X. MX ≅XXCorresponding parts of XXXXXXXXX triangles are XXXXXXXXX
8.XXXXX X is XXXXXXXXXXXX from theXXXXXXXXXX XX XXXXXXXXXXXX
sides of ∠XXX
.
m∠JNM = m∠XXX....................................Opposite XXXXXX
4x+6 = 7x-21
7x-4x = X+21
3x = XX
x = XX/3 = 9
m∠XXX = 4x + 6 = X*9 + X =XXo
△ABC = △JKL.............................................Congruent
m∠A = m∠J , m∠X= m∠X, and m∠C = m∠X
So, m∠K = m∠B = 55o
m∠X = 25o
XX △XXX :
m∠J = XXXo –( m∠X + m∠X) = 180o –( XXo + 25o)= 100o
△ABC XXX △DEFCongruent .................. △XXX map XX △DEF by a
reflection across y XXXX XXXXXXXX by a XXXXXXXXXX across x axis
△XXX XXX △JKLNot Congruent .......... because XXXXX XX no sequence of rigid XXXXXXX that XXXX △XXX to △JKL
△XXX XXX △XXXXXXXXXXXX .................. △ABC map XX △XXX XX a XXXXXXXXXX across y XXXX
△XXX and △XXXXXX XXXXXXXXX .......... because there XX no sequence of XXXXX XXXXXXX XXXX maps △JKL to △DRF
△JKL and △XXX Not XXXXXXXXX .......... because there XX no XXXXXXXX XX XXXXX motions XXXX maps △XXX XX △XXX
△XXX XXX △DEFXXXXXXXXX ................△QRS map to△XXX
XX a XXXXXXXXXX XXXXXX x XXXX
△XXX isXXX congruent XX △XYZ, XXXXXXX XXXXX XX no XXXXXXXX of XXXXX XXXXXXX that XXXX △PQR XX △XYZ.
XXXXXXX△NBG ≅ △XXX
Points N,X and X coincide with XXX XXXXXX W,T XXX S respectively after XXXXXXX. XX,
NG ↔ XX
XX ↔XX
∠X ↔∠S
∠N ↔∠X
△XXX ≅△XXX....................XXX vertices X,X,Xcoincide with the points M, C, X XXXXXXXXXXXX XXXXX XXXXXXX.
Number the XXXXX XXXXX containing XXXXX XXXX1 XX X.
The XXXXXXX XXXXXXXX XX XXXXX from XXXXX to finsh as :
X -&XX;1 ->X ->X -&XX;6 -&XX;4
XXXXXXXXXXXXX X and XXXXXXXXXXXXX X Not XXXXXXXXX
XXXXXXXXXXXXX X and quadrilateral X Not Congruent
XXXXXXXXXXXXX X and XXXXXXXXXXXXX X Not Congruent
XXXXXXXXXXXXX 2 and quadrilateral 3 Congruent........XXXXXXXXXX XXXXXX x XXXX XXXXXXXX XX 1down
XXXXXXXXXXXXX X and quadrilateral X Congruent........XXXXXXXXXX XXXXXX
x axis XXXXXXXX by XXXXXXXXXX XXXXXX y XXXX XXXXXXXX XX 180o XXXXXXXX XXXXXXXX XX 1down.
XXXXXXXXXXXXX 3 XXX quadrilateral 4 XXXXXXXXX........XXXXXXXXXX XXXXXX
y axis XXXXXXXX XX 180o XXXXXXXX.
Congruent : (x,y) -&XX; (x+3, y-X) ...............Translate XXXXX 3 XXXXX and XXXX
4 units
(x, y) -&XX; (-x, -y) ..................reflection XXXXXX x XXXX followed by
reflection XXXXXX y axis
Not XXXXXXXXX :
(x,y)-&XX; ( 3x,XX)...................Dilation with scale XXXXXX X
(x, y) -&XX; (X,XX).....................XXXXXXXXX left x units followed by
XXXXXXXX XX XXXXX XXXXXX 4
(x,y)-> ( x/3,y/X)...................Dilation XXXX XXXXX factor 1/X
">