중2-2수학 [1강] 이등변삼각형의 성질(1) 중2수학 중간고사 기말고사

Main ideas & lessons (isosceles triangle properties)

• The lesson builds on earlier (elementary) knowledge and extends it to middle school problem-solving, including the why behind properties (proof is deferred for later).
• An isosceles triangle is defined as a triangle with two equal sides.

Key terminology (for non-equilateral isosceles triangles)

• The two equal sides meet at the vertex.
• The angles at the bottom (adjacent to the base) are called base angles.
• The angle formed at the top (where the equal sides meet) is the vertex angle.
• The remaining side (not one of the equal sides) is the base.

Two central properties used repeatedly

1. The angle bisector of the vertex angle:
   • splits the base into two equal parts
   • meets the base perpendicularly
2. The two base angles are equal in measure.

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Core geometry fact used: “exterior/flag formula” (linear pair / exterior angle idea)

The teacher repeatedly uses a triangle-angle relationship often taught as an exterior angle fact:

• The measure of an exterior angle equals the sum of the measures of the two remote (non-adjacent) interior angles.

Equivalent working methods shown:

• Angles on a straight line add to 180°, so:
  • you can find an interior angle by subtracting from 180°
• Then use division when base angles are equal.

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Instructional workflow demonstrated for solving problems

A) Given two equal sides (AB = AC)

• Since base angles are equal, the two base angles are identical.
• Steps shown:
  • Use the 180° total triangle sum to compute a key angle:
    • If one angle is given (e.g., 40°), then the other two add to 180° − 40°
    • If those two are equal base angles, divide by 2
  • Once one angle is found, use triangle sums again to find the other angles in the diagram.

B) When the problem asks for multiple angles (labeled a, b, d, etc.)

A typical pattern:

• Find a key angle using base-angle equality (often by subtracting from 180° and dividing).
• Use angle sums and/or linear pairs to compute adjacent angles.
• Reuse equality constraints to transfer a computed angle to its matching angle.

C) When two isosceles triangles are nested/connected in a larger diagram

Use:

• Base-angle equalities inside each isosceles triangle
• The exterior/flag formula to relate angles across shared lines

Repeated “flag formula” pattern:

• Express each relevant angle in terms of x
• Use exterior = sum of remote interior angles to form an equation like:
  • (sum of expressions) = given exterior (e.g., 80°)
• Solve for x, then substitute to get all requested angles.

D) Most common/most difficult cases (two-step algebra with x)

Example pattern:

• Let some angles be x
• Use the isosceles/angle-bisector structure to infer angles as x, 2x, 3x, etc.
• Apply the exterior/flag formula to build an equation such as:
  • 4x = 80°
• Solve:
  • x = 20°

Another example pattern:

• Use labeled angles (a, b) and a given degree:
  • Assign variables to unknown angles
  • Use flag formula to write expressions like EB = 2a + 48
  • Use a second flag relationship to link variables (e.g., b = a + x or similar)
  • Substitute and solve for x (example yields x = 24°)

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Speaker / sources featured

• Teacher Renji (the instructor)
• Dan-guri friends (addressed as the student audience; not an additional speaker)