Isosceles Trapezoid Property: Analyzing Base Angle Relationships

Trapezoid Properties with Base Angle Analysis

True OR False:

In all isosceles trapezoids the base Angles are equal.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Are the base angles equal in every isosceles trapezoid? Let's find out!
00:10 The given data tells us the sides are equal. Interesting, right?
00:15 Now, let's draw the diagonals of the trapezoid. Visualize the lines from opposite corners.
00:29 Notice how the diagonals are equal in length. That's key!
00:39 We see that triangles are congruent by the S.A.S. Rule. That's Side, Angle, Side.
00:51 So, the corresponding angles are equal by congruence. Aha!
01:01 And that's how we solve this problem! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

True OR False:

In all isosceles trapezoids the base Angles are equal.

2

Step-by-step solution

True: in every isosceles trapezoid the base angles are equal to each other.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Definition: Isosceles trapezoids have equal legs and equal base angles
  • Property: Both base angles measure exactly the same degree value
  • Verification: Check that opposite angles are supplementary and base angles match ✓

Common Mistakes

Avoid these frequent errors
  • Confusing base angles with all angles being equal
    Don't assume all four angles in an isosceles trapezoid are equal = wrong conclusion! Only the base angles (same base) are equal, while opposite angles are supplementary. Always remember that base angles are equal, but adjacent angles add to 180°.

Practice Quiz

Test your knowledge with interactive questions

True OR False:

In all isosceles trapezoids the base Angles are equal.

FAQ

Everything you need to know about this question

What exactly are the 'base angles' in an isosceles trapezoid?

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The base angles are the two angles that touch the same parallel side (base). In an isosceles trapezoid, the angles touching the longer base are equal, and the angles touching the shorter base are also equal to each other.

Are all four angles in an isosceles trapezoid the same?

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No! Only the base angles are equal. The angles on the longer base are equal to each other, and the angles on the shorter base are equal to each other, but these two pairs have different measures.

How can I remember which angles are equal?

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Think of it this way: angles that sit on the same base (same parallel side) are equal. So if you have bases AB and CD, then angles A and B are equal, and angles C and D are equal.

Do the base angles add up to 180°?

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No, but adjacent angles do! Each base angle plus the angle next to it (on the leg) equals 180°. This is because the legs are parallel to each other in an isosceles trapezoid.

Is this property true for all trapezoids?

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No, only for isosceles trapezoids! Regular trapezoids don't have this property. The key is that isosceles trapezoids have equal legs, which creates the equal base angles.

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