8th Grade
How do you use informal arguments to establish facts about the angle sum of a triangle?
{
"voice_prompt": "",
"manuscript": {
"title": {
"text": "How do you use informal arguments to establish facts about the angle sum of a triangle?",
"audio": "How do you use informal arguments to establish facts about the angle sum of a triangle?"
},
"description": {
"text": "You can show that the angle sum of any triangle is 180 degrees using this approach: arrange three copies of the internal angles so that they fit together and form a straight line.",
"audio": "You can show that the angle sum of any triangle is 180 degrees using this approach: arrange three copies of the internal angles so that they fit together and form a straight line."
},
"scenes": [
{
"text": "Let\u2019s explore how this works.",
"latex": ""
},
{
"text": "Start by drawing a triangle. The shape doesn\u2019t matter.",
"latex": ""
},
{
"text": "Take a closer look at each of the vertices. These are the angles inside the triangle.",
"latex": ""
},
{
"text": "Next, trace each angle and move them so their points all touch and the sides line up.",
"latex": ""
},
{
"text": "What do you notice? The three angles fit together to form a straight line. And a straight line is 180 degrees.",
"latex": ""
},
{
"text": "That shows you something useful \u2014 the three angles add up to 180 degrees. This is true for all triangles, no matter their shape or size.",
"latex": ""
},
{
"text": "A powerful result of this is that if you know two angles in a triangle, you can use the 180-degree rule to figure out the third one.",
"latex": ""
},
{
"text": "Like in this triangle: if one angle is 40 degrees and another is 60 degrees, the third angle must be 80 degrees \u2014 because 40 plus 60 plus 80 makes 180.",
"latex": ""
}
],
"outro": {
"text": "You can show that the angle sum of any triangle is 180 degrees using this approach: arrange three copies of the internal angles so that they fit together and form a straight line.",
"audio": "You can show that the angle sum of any triangle is 180 degrees using this approach: arrange three copies of the internal angles so that they fit together and form a straight line."
}
}
}
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Displaying en_8_geo_triangle_informal_angle_sum.json.
