Question

identifying triangles
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write the letter or letters that match each statement.
1 has perpendicular line segments
2 has an obtuse angle
3 has right angles
4 has acute angles
5 has more than one kind of angle
6 has only one kind of angle
7 does not have any right angles
8 is a right triangle
practice
9 list all the factors of 12.
10 name the next 4 multiples of 7. 35,

Explanation:

Step1: Analyze each triangle

• Right - angled triangle: A triangle with one right angle (\(90^{\circ}\)). Right - angled triangles have perpendicular line segments (the two legs forming the right angle).
• Obtuse - angled triangle: A triangle with one obtuse angle (an angle greater than \(90^{\circ}\) but less than \(180^{\circ}\)).
• Acute - angled triangle: A triangle with all acute angles (angles less than \(90^{\circ}\)).

For statement ① (Has perpendicular line segments)

• Right - angled triangles (C and D) have perpendicular line segments (the two sides forming the right angle). So the answer is \(C,D\).

For statement ② (Has an obtuse angle)

• Obtuse - angled triangles (E and F) have one obtuse angle. So the answer is \(E,F\).

For statement ③ (Has right angles)

• Right - angled triangles (C and D) have right angles. So the answer is \(C,D\).

For statement ④ (Has acute angles)

• All triangles (A, B, C, D, E, F) have acute angles. In a right - angled triangle, the other two angles are acute. In an obtuse - angled triangle, the other two angles are acute. In an acute - angled triangle (B), all three angles are acute. So the answer is \(A,B,C,D,E,F\).

For statement ⑤ (Has more than one kind of angle)

• Right - angled triangles (C, D) have one right angle and two acute angles. Obtuse - angled triangles (E, F) have one obtuse angle and two acute angles. So the answer is \(C,D,E,F\).

For statement ⑥ (Has only one kind of angle)

• Acute - angled triangle (B) has all acute angles. So the answer is \(B\).

For statement ⑦ (Does NOT have any right angles)

• Acute - angled triangle (B) and obtuse - angled triangles (E, F) do not have right angles. So the answer is \(A,B,E,F\).

For statement ⑧ (Is a right triangle)

• Right - angled triangles (C and D) are right triangles. So the answer is \(C,D\).

Step2: Find factors of 12

• Factors of a number \(n\) are the numbers that divide \(n\) evenly.
• \(12\div1 = 12\), \(12\div2=6\), \(12\div3 = 4\), \(12\div4=3\), \(12\div6 = 2\), \(12\div12=1\).
• The factors of 12 are \(1,2,3,4,6,12\).

Step3: Find next 4 multiples of 7 after 35

• Multiples of 7 are of the form \(7\times k\), where \(k\) is an integer.
• If \(7\times5 = 35\), then \(7\times6=42\), \(7\times7 = 49\), \(7\times8=56\), \(7\times9 = 63\).

Answer:

1. \(C,D\)
2. \(E,F\)
3. \(C,D\)
4. \(A,B,C,D,E,F\)
5. \(C,D,E,F\)
6. \(B\)
7. \(A,B,E,F\)
8. \(C,D\)
9. \(1,2,3,4,6,12\)
10. \(42,49,56,63\)