Download Theorem - Powell County Schools

Geometry
Triangle Theorems
When an isosceles triangle has exactly two congruent sides, these two sides are the
________. The angle formed by the legs is the __________________________.
The third side is the ________________of the isosceles triangle.
The two angles adjacent to the base are called ___________________________.
 __________________________ Theorem
If two sides of a triangle are ________________, then the angles_________
them are ______________________.
 Converse of _______________________Theorem
If two angles of a triangle are ___________________, then the sides
______________________ them are __________________.
 Example 1: Using the Base Angles Theorem,
̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐵 ⟹ ___________ ≅ ___________
 Example 2: If ∠𝐷 ≅ ∠𝐸, then ________________________.
 Example 3: What is the measure of ∠𝑥 𝑎𝑛𝑑 ∠𝑦?
 Example 4: Solve for x.
 Example 5: Solve for x.
A _______________________ of a triangle is a segment that connects the
midpoints of two sides of the triangle. Every triangle has _________midsegments.
 Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is ________
to the third side and is ____________________________ that side.
̅̅̅̅ is a midsegment of triangle ABC. Find the value of x.
 Example 6: 𝐷𝐸
̅̅̅̅ is a midsegment of triangle ABC. Find the value of x.
 Example 7: 𝐷𝐸
̅̅̅̅ is a midsegment of triangle ABC. Find the value of x.
 Example 8: 𝐷𝐸
 Example 9: Use ∆𝐺𝐻𝐽, where A, B, and C are midpoints of the sides. If
𝐴𝐵 = 3𝑥 + 8 and 𝐺𝐽 = 2𝑥 + 24, what is 𝐴𝐵?
 Example 10: Use ∆𝐺𝐻𝐽, where A, B, and C are midpoints of the sides. If
𝐴𝐶 = 3𝑦 − 5 and 𝐻𝐽 = 4𝑦 + 2, what is 𝐻𝐵?
A _____________ of a triangle is a segment from a vertex to the midpoint of the
opposite side. The three medians of a triangle are _________________. The point
of concurrency, called the ________________, is inside the triangle.
 Concurrency of Medians of a Triangle
The medians of a triangle intersect at a point that is ___________________
of the distance from _______________ to the midpoint of the opposite side.
 Example 11: In ∆𝑅𝑆𝑇, 𝑄 is the centroid and 𝑆𝑄 = 8. Find 𝑄𝑊 and 𝑆𝑊.
 Example 12: There are three paths through a triangular park. Each path goes
from the midpoint of one edge to the opposite corner. The paths meet at
point P.
a) If SC = 2100 feet, find PS and PC.
b) If BT = 1000 feet, find TC and BC.
c) If PT = 800 feet, find PA and TA.