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ABC is an isosceles triangle. (i) Measure the size of angles B and C. What do you notice? (ii) Without measuring it, look at the size of A. Do you think it is the same size as B or C?

Mathematics

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Part a(i)· 2 steps

Measure the size of angles B and C. What do you notice?

  1. Identify the type of triangle.

    The tick marks on sides AB and AC indicate that △ABC\triangle ABC is an isosceles triangle, meaning sides AB and AC are equal in length.

  2. Apply the property of an isosceles triangle.

    In an isosceles triangle, the angles opposite the equal sides are equal. Angle B is opposite side AC, and Angle C is opposite side AB. Therefore, if you were to measure them, you would notice that Angle B and Angle C are equal\boxed{\text{Angle B and Angle C are equal}}.

Part a(ii)· 2 steps

Without measuring it, look at the size of A. Do you think it is the same size as B or C?

  1. Visually inspect the angles.

    By looking at the diagram, ∠A\angle A appears to be larger than ∠B\angle B or ∠C\angle C.

  2. Recall properties of isosceles triangles.

    In an isosceles triangle, the base angles (angles B and C, which are opposite the equal sides) are equal. The vertex angle (angle A) is typically different from the base angles, unless it's an equilateral triangle.
    No, I do not think ∠A\angle A is the same size as ∠B\angle B or ∠C\angle C. It appears to be larger\boxed{\text{larger}}.

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