A classic angle chasing problem | Geometry | 84
In this video, we solve a nice geometry problem. At the end of the video, an exercise is included for viewers to try on their own.
Check out this playlist which is a collection of geometry problems.
• Geometry
Timecodes
0:00 - Description of the problem
0:37 - Use the triangle inequality to show that ∠A is less than 2θ, then apply the angle sum property to demonstrate that 6θ is less than 180°
1:43 - Construct a triangle PAC such that ∠ACP = 2θ
2:00 - Join D to P and drop perpendiculars DQ, DR and DS to the lines PB, BC and CP, respectively
2:18 - Show that triangle BDQ is congruent to triangle BDR by using the AAS congruence postulate and then use the property that corresponding parts of congruent triangles are congruent to show that DQ = DR
2:54 - Show that triangle DRC is congruent to triangle DSC by using the AAS congruence postulate and then use the property that corresponding parts of congruent triangles are congruent to show that DS = DR
3:31 - Show that triangle DPQ is congruent to triangle DPS by using the HL congruence postulate and then use the property that corresponding parts of congruent triangles are congruent to show that ∠DPQ = ∠DPS
4:22 - Use the exterior angle theorem to show that ∠PAC = 4θ
4:44 - Construct a triangle DPT such that PT = PA
4:54 - Show that triangle DPT is congruent to triangle DPA by using the SAS congruence postulate and then use the property that corresponding parts of congruent triangles are congruent to show that DT = DA = y and ∠PTD = ∠PAD = 4θ
5:40 - Extend side BD to intersect PC at M
5:50 - Show that triangle MDT is similar to triangle MBC by using the AA similarity criterion
6:22 - Use the property that corresponding sides in similar triangles are proportional to show that a = y
6:54 - Use the exterior angle theorem to show that ∠BMP = 5θ
7:07 - Use the property that the base angles of isosceles triangle BMT are equal to show that θ = 20°
7:49 - An exercise for viewers to try
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