Answer:
see below
Step-by-step explanation:
1. m∠DEF = m∠_FEK___ = 44° = Def. of ∠ bisector
2. m∠DEK = m∠_DEF___+m∠FEK___= _angle addition postulate________________
3. m∠DEK = _44___ + _44___ = 88° = Substitution, Algebra
4. DE = _KE____ = Given
5. EF = _FE____ = Reflexive property
6. △DEF ≅ △_KEF____ = _SAS postulate________________
7. DF = FK_____ = ___CPCTC (corresponding parts of congruent triangles are congurent)______________
8. KF = 1/2DK =8 _____ = Algebra, 7
The opposite side of the 11cm will also be 11cm and the 2 others will both be 8 cm.
Answer:
x=9
Step-by-step explanation:
We can use similar triangles and ratios. Put the small triangle side over the large triangle side.
9cm 3x -20
---------- = ---------------- We need to add the sides to get to the larger triangle
72+9 cm 3x-20 + 56
We can cross multiply to solve
9 * (3x-20+56) = (72+9) * (3x-20)
Simplify
9*(3x+36) = 81*(3x-20)
Distribute
27x +324 = 243x -1620
Subtract 27x from each side
27x-27x +324 = 243x-27x -1620
324 = 216x-1620
Add 1620 to each side
324+1620 = 216x
1944 = 216x
Divide each side by 216
1944/216 = 216x/216
9=x
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