Exterior Angle Of An Isosceles Triangle
A step-by-step visual walkthrough of a psychometric-style geometry problem: an isosceles triangle ABC with AB = AC, angle BAC = 40°, and BC extended to D. The animation isolates one fact at a time, using base angle equality and the exterior angle theorem to build toward angle ACD = 110°, before revealing the answer. Useful for students practicing timed geometry reasoning and exterior angle relationships.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a polished 16:9 mathematical teaching animation for a psychometric-exam geometry question. Audience: Students preparing for the Israeli Psychometric Exam. Teaching philosophy: Do NOT simply show the solution. The animation must deliberately control the student's visual attention and reveal one atomic insight at a time. At every moment, visually emphasize only the information needed for the current inference and de-emphasize irrelevant information. Visual style: - Premium minimalist mathematical animation - Dark charcoal background - Clean thin geometry lines - Large readable mathematical labels - Smooth, deliberate motion - No decorative animation - No cartoon characters - No handwriting - No unnecessary text - Use color only to direct attention - Keep the diagram mathematically accurate - Leave enough empty space for clarity - Do not show the final answer before the reasoning is complete QUESTION: Triangle ABC is isosceles with AB = AC. Angle BAC = 40 degrees. BC is extended beyond C to point D. Find the exterior angle ACD. Answer choices: 70°, 90°, 110°, 140°. Correct answer: 110°. ANIMATION STORYBOARD: SCENE 1 — Present the problem Draw triangle ABC centered slightly left of the screen. A should be at the top, B bottom-left, C bottom-right. Extend BC beyond C to point D. Show: AB = AC angle BAC = 40° and mark the unknown exterior angle ACD with x°. Briefly show the four answer choices on the right. Do not solve anything yet. Pause. SCENE 2 — First atomic clue Dim everything except sides AB and AC. Highlight AB and AC simultaneously. Place identical tick marks on AB and AC. Do not highlight any angles yet. Display a very short caption: "AB = AC" Pause so the student notices the relationship. SCENE 3 — Convert clue into inference Keep AB and AC subtly highlighted. Now highlight angle ABC and angle BCA using identical arcs. Animate the idea visually: equal sides → equal opposite angles. Display: ∠B = ∠C Do NOT calculate their values yet. This is the first hidden idea the student must learn to notice. SCENE 4 — Bring back the 40° clue Dim the equal-side markings slightly. Highlight only angle A and its 40° label. Then show the triangle angle sum: ∠A + ∠B + ∠C = 180° Transform it into: 40° + ∠B + ∠C = 180° Since ∠B = ∠C, smoothly transform into: 40° + 2∠C = 180° Then: 2∠C = 140° Then: ∠C = 70° As ∠C = 70° appears algebraically, simultaneously change the angle label at C from an unlabeled arc to 70°. SCENE 5 — Second atomic visual insight Remove or strongly dim the algebra. Focus the camera/attention on vertex C. Highlight: - ray CB - ray CD Make it visually obvious that B-C-D form one straight line. Highlight the interior 70° angle BCA. Then highlight the adjacent exterior angle ACD labeled x°. Show a subtle straight-angle arc or visual cue. Display: 70° + x = 180° Then transform smoothly: x = 180° - 70° x = 110° SCENE 6 — Answer Highlight only: ∠ACD = 110° Bring back the answer choices and visually select: 110°. Then briefly reconstruct the entire reasoning chain visually: AB = AC ↓ ∠B = ∠C ↓ ∠C = 70° ↓ straight line at C ↓ x = 110° FINAL TEACHING MOMENT: Return to the original unsolved diagram for one second. Highlight AB and AC again, then angle B and angle C. Display: "Notice the clue before calculating." The purpose is to train the student to recognize the hidden geometric relationship, not merely memorize the calculation. Timing: Approximately 45–60 seconds total. Use pauses of roughly 0.5–1.5 seconds after important visual discoveries. Never introduce two new ideas simultaneously. Audience: Student Teaching plan: Goal: Train the student to notice hidden geometric clues before calculating. Question: In isosceles triangle ABC, AB = AC and angle A = 40°. BC is extended beyond C to D. Find exterior angle ACD. Teaching sequence: 1. Show the complete problem without solving it. 2. First atomic insight: Direct attention only to AB and AC. Dim everything else. Ask visually: What does AB = AC tell us? 3. Reveal the hidden consequence: Equal sides imply equal opposite angles. Highlight angles B and C together. Show: ∠B = ∠C 4. Bring attention back to the 40° angle. Use the triangle angle sum: 40° + B + C = 180° Since B = C: 40° + 2C = 180° C = 70° 5. Second atomic insight: Shift attention to vertex C. Highlight B-C-D as a straight line. Highlight the 70° interior angle and exterior angle x. Make the student notice that they form 180°. 6. Solve: 70° + x = 180° x = 110° 7. End by briefly returning to the original diagram. Highlight AB = AC again and then angles B and C. Final takeaway: The important skill is not the calculation. It is noticing that equal sides immediately give equal opposite angles. Visual principle: Reveal only ONE new idea at a time. Dim irrelevant information. Use highlighting to control where the student's eyes should look. Pause briefly before revealing each inference.
Make the next one in this series
- Show why the exterior angle equals the sum of the two remote interior angles with a general proof
- Animate the same triangle with a different vertex angle to test the pattern numerically
- Create a follow-up problem using exterior angles in a triangle with two unknown base angles
