9514 1404 393
Answer:
- x = 7
- x = 1.2
Step-by-step explanation:
1. Sides with the same mark are congruent:
7x -4 = 31
7x = 35 . . . . . . add 4
x = 5 . . . . . . . . divide by 7
Similarly, ...
4y +8 = 24 . . . sides with 3 hash marks are the same length
y +2 = 6 . . . . . divide by 4
y = 4 . . . . . . . . subtract 2
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2. The (corresponding) right angles at B and D are congruent, and the angle at A is congruent with itself. This means triangles ABC and ADE are similar by the AA theorem. (Your flow chart might be: (show 2 angles the same) → (claim AA similarity).)
Similar triangles have corresponding sides in the same ratio:
x/3 = (x+4)/13
13x = 3(x +4) . . . . . . multiply by 3×13
10x = 12 . . . . . . . . . . subtract 3x
x = 1.2 . . . . . . . . divide by 10
