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0.8 rriangles
Date

qquad

qquad 10, ind the range of 
qquad Nothe length for 
bar(AB),
Solve for 
m bar(AB).

{:[m bar(AB) < 5+9rarrm bar(AB)],[m bar(AB) > 9-5rarrm bar(AB)]:}
50 the length for 
bar(AB) is between 
4cm and 
14cm, or 
4cm < m bar(AB) < 14cm.
Qlsoify each triangle by angles and sides.
01.
3.
4.

{:[" obtuse triangle "],[" scalene triangle "]:}

qquad

qquad

qquad
The measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.
: 
30^(@),65^(@)
6. 
73^(@),37^(@),
7. 
60^(@),60^(@),
8. 
108^(@),32^(@),

180^(@)-(30^(@)+65^(@))=85^(@) sute triangle 
qquad

qquad

qquad ilar pes the
9. 
56^(@),19^(@),
10. 
30^(@),30^(@),
11. 
90^(@),45^(@),
12. 
100^(@),36^(@),

qquad

qquad

qquad

qquad

00.88 rriangles\newlineDate\newline \qquad \newline \qquad 1010, ind the range of \qquad Nothe length for AB \overline{A B} ,\newlineSolve for mAB \mathrm{m} \overline{A B} .\newlinemAB<5+9mAB mAB>95mAB \begin{array}{l} \mathrm{m} \overline{A B}<5+9 \rightarrow \mathrm{m} \overline{A B} \\ \mathrm{~m} \overline{A B}>9-5 \rightarrow \mathrm{m} \overline{A B} \end{array} \newline5050 the length for AB \overline{A B} is between 4 cm 4 \mathrm{~cm} and 14 cm 14 \mathrm{~cm} , or 4 cm<mAB<14 cm 4 \mathrm{~cm}<\mathrm{m} \overline{A B}<14 \mathrm{~cm} .\newlineQlsoify each triangle by angles and sides.\newline0101.\newline33.\newline44.\newline obtuse triangle  scalene triangle  \begin{array}{l} \text { obtuse triangle } \\ \text { scalene triangle } \end{array} \newline \qquad \newline \qquad \newline \qquad \newlineThe measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.\newline: \qquad 22\newline66. \qquad 33,\newline77. \qquad 44,\newline88. \qquad 55,\newline \qquad 66 sute triangle \qquad \newline \qquad \newline \qquad ilar pes the\newline99. \qquad 00,\newline1010. \qquad 11,\newline1111. \qquad 22,\newline1212. \qquad 33,\newline \qquad \newline \qquad \newline \qquad \newline \qquad

Full solution

Q. 00.88 rriangles\newlineDate\newline \qquad \newline \qquad 1010, ind the range of \qquad Nothe length for AB \overline{A B} ,\newlineSolve for mAB \mathrm{m} \overline{A B} .\newlinemAB<5+9mAB mAB>95mAB \begin{array}{l} \mathrm{m} \overline{A B}<5+9 \rightarrow \mathrm{m} \overline{A B} \\ \mathrm{~m} \overline{A B}>9-5 \rightarrow \mathrm{m} \overline{A B} \end{array} \newline5050 the length for AB \overline{A B} is between 4 cm 4 \mathrm{~cm} and 14 cm 14 \mathrm{~cm} , or 4 cm<mAB<14 cm 4 \mathrm{~cm}<\mathrm{m} \overline{A B}<14 \mathrm{~cm} .\newlineQlsoify each triangle by angles and sides.\newline0101.\newline33.\newline44.\newline obtuse triangle  scalene triangle  \begin{array}{l} \text { obtuse triangle } \\ \text { scalene triangle } \end{array} \newline \qquad \newline \qquad \newline \qquad \newlineThe measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.\newline: \qquad 22\newline66. \qquad 33,\newline77. \qquad 44,\newline88. \qquad 55,\newline \qquad 66 sute triangle \qquad \newline \qquad \newline \qquad ilar pes the\newline99. \qquad 00,\newline1010. \qquad 11,\newline1111. \qquad 22,\newline1212. \qquad 33,\newline \qquad \newline \qquad \newline \qquad \newline \qquad
  1. Range of mˉAB\bar{m}AB: First, let's solve for the range of mˉAB\bar{m}AB. Using the inequalities given: mˉAB<5+9\bar{m}AB < 5 + 9 and mˉAB>95\bar{m}AB > 9 - 5.
  2. Upper limit calculation: Calculate the upper limit:\newline5+9=145 + 9 = 14.\newlineSo, mˉAB<14\bar{m}AB < 14 cm.
  3. Lower limit calculation: Calculate the lower limit:\newline95=49 - 5 = 4.\newlineSo, mˉAB>4\bar{m}AB > 4 cm.
  4. Combine inequalities for mABm \overline{AB}: Combine the two inequalities to get the range for mABm \overline{AB}:4cm<mAB<14cm4 \, \text{cm} < m \overline{AB} < 14 \, \text{cm}.
  5. Classification of first triangle: Now, let's classify the triangles by angles.\newlineFor the first triangle with angles 3030^\circ and 6565^\circ:\newline180(30+65)=85180^\circ - (30^\circ + 65^\circ) = 85^\circ.
  6. Third angle calculation for first triangle: The sum of angles in a triangle is 180°180°, so the third angle is 85°85°. This makes it an acute triangle since all angles are less than 90°90°.
  7. Classification of second triangle: For the second triangle with angles 73°73° and 37°37°: 180°(73°+37°)=70°180° - (73° + 37°) = 70°.
  8. Third angle calculation for second triangle: The sum of angles in a triangle is 180180^\circ, so the third angle is 7070^\circ. This also makes it an acute triangle.
  9. Classification of third triangle: For the third triangle with angles 60°60° and 60°60°: 180°(60°+60°)=60°180° - (60° + 60°) = 60°.
  10. Third angle calculation for third triangle: The third angle is also 6060^\circ, making this an equilateral triangle, which is a special case of an acute triangle.
  11. Classification of fourth triangle: For the fourth triangle with angles 108°108° and 32°32°:\newline180°(108°+32°)=40°180° - (108° + 32°) = 40°.
  12. Third angle calculation for fourth triangle: The third angle is 4040^\circ, and since one angle is greater than 9090^\circ, this is an obtuse triangle.
  13. Classification of fifth triangle: For the fifth triangle with angles 56°56° and 19°19°:\newline180°(56°+19°)=105°180° - (56° + 19°) = 105°.
  14. Third angle calculation for fifth triangle: The third angle is 105105^\circ, which makes this an obtuse triangle as well.
  15. Classification of sixth triangle: For the sixth triangle with angles 3030^\circ and 3030^\circ: 180(30+30)=120180^\circ - (30^\circ + 30^\circ) = 120^\circ.
  16. Classification of sixth triangle: For the sixth triangle with angles 3030^\circ and 3030^\circ: 180(30+30)=120180^\circ - (30^\circ + 30^\circ) = 120^\circ.The third angle is 120120^\circ, which is an error because the sum of the first two angles already exceeds 180180^\circ.

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