Of course! Let's solve the problems on this worksheet step by step.
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##
Section A: Two Triangles
Task: Split each quadrilateral into two triangles.
This is a hands-on drawing task. To do this, you need to draw one diagonal line (a straight line connecting two opposite corners) inside each quadrilateral. This will divide it into exactly two triangles.
How to do it:
- Pick any quadrilateral.
- Use your ruler and pencil to draw a straight line from one corner to the opposite corner (not adjacent).
- You now have two triangles!
- Repeat for all 7 quadrilaterals shown.
> *Note: Since I can't draw on the image, I’ll describe it: For example, in the first diamond shape, draw a line from the top point to the bottom point — that splits it into two triangles. In a rectangle, draw from top-left to bottom-right.*
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Complete these sentences:
1.
The sum of angles in a triangle is _180°_.
>
✔ Explanation: This is a fundamental rule in geometry. No matter what type of triangle (equilateral, isosceles, scalene, right, obtuse, acute), the three interior angles always add up to
180 degrees.
2.
A quadrilateral can be split into _two_ triangles.
>
✔ Explanation: As shown in the activity, drawing one diagonal divides any quadrilateral (4-sided polygon) into exactly two triangles.
3.
So, the sum of angles in a quadrilateral must be _360°_.
>
✔ Explanation: Since a quadrilateral = 2 triangles, and each triangle has 180°, then:
>
> `180° + 180° = 360°`
>
> So, the total of all four interior angles in any quadrilateral is always
360 degrees.
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##
Section B: Match the missing angle to each quadrilateral.
We are given 4 quadrilaterals with 3 angles labeled, and we need to find the missing 4th angle. We use the fact that
the sum of all interior angles in a quadrilateral is 360°.
Let’s calculate each one:
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Quadrilateral 1 (Blue Parallelogram)
Given angles: 70°, 110°, 110°
Missing angle = 360° - (70° + 110° + 110°)
= 360° - 290°
=
70°
✔ Answer: 70°
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Quadrilateral 2 (Pink Rectangle)
Given angles: 90°, 90°, 90°
Missing angle = 360° - (90° + 90° + 90°)
= 360° - 270°
=
90°
✔ Answer: 90°
*(Note: All angles in a rectangle are 90°, so this makes sense.)*
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Quadrilateral 3 (Green Trapezoid)
Given angles: 108°, 108°, 72°
Missing angle = 360° - (108° + 108° + 72°)
= 360° - 288°
=
72°
✔ Answer: 72°
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Quadrilateral 4 (Purple Parallelogram)
Given angles: 65°, 65°, 115°
Missing angle = 360° - (65° + 65° + 115°)
= 360° - 245°
=
115°
✔ Answer: 115°
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##
✔ Final Matching Answers for Section B:
- Blue parallelogram →
70°
- Pink rectangle →
90°
- Green trapezoid →
72°
- Purple parallelogram →
115°
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## 📝 Summary of All Answers:
Section A Sentences:
1. The sum of angles in a triangle is
180°.
2. A quadrilateral can be split into
two triangles.
3. So, the sum of angles in a quadrilateral must be
360°.
Section B Matching:
- Blue quad →
70°
- Pink quad →
90°
- Green quad →
72°
- Purple quad →
115°
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You’re all set! Just remember:
Triangles = 180°, Quadrilaterals = 360°, and splitting them helps prove why. 😊
Parent Tip: Review the logic above to help your child master the concept of triangles and quadrilaterals worksheet.
