Using the definition of congruent triangles, the missing measurements are:
23. m = 7; LO = 14; NO = 14
24. x = 15; m∠QTS = 90°
25. p = 3; IJ = 15; KJ = 15
26. r = 3; UW = 48
27. y = 7; m∠DEF = 50°
28. m = 5; p = 10
<h3>What are Congruent Triangles?</h3>
If two triangles are congruent, then all its corresponding sides and angles are equal.
23. The two triangles are congruent by SAS, therefore:
LO = NO
m + 7 = 2m
7 = 2m - m
7 = m
m = 7
LO = NO = m + 7 = 7 + 7 = 14
LO = 14
NO = 14
24. But triangles are congruent by SSS, therefore:
3x = 5x - 30
3x - 5x = -30
-2x = -30
x = 15
m∠QTS = 2(3x) = 6x = 6(15)
m∠QTS = 90°
25. Both triangles are congruent by ASA, therefore:
4p + 3 = 3p + 6
4p - 3p = -3 + 6
p = 3
IJ = KJ = 4p + 3 = 4(3) + 3 = 15
IJ = 15
KJ = 15
26. The two triangles are congruent by SAS, therefore:
5r + 9 = 8r
9 = 8r - 5r
9 = 3r
9/3 = r
r = 3
UW = 2(8r) = 16r = 16(3)
UW = 48
27. Both triangles are congruent by SSS, therefore:
3y + 4 = 5y - 10
3y - 5y = -4 - 10
-2y = -14
y = 7
m∠DEF = 2(3y + 4) = 6y + 8 = 6(7) + 8
m∠DEF = 50°
28. Both triangles are congruent by SSS, therefore:
2m = 10
m = 10/2
m = 5
2p - 5 = p + 5
2p - p = 5 + 5
p = 10
Learn more about congruent triangles on:
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