Guided Notes – SRT.4
Proportional Parts within Triangles In any triangle, a
line parallel to one side of a triangle separates the other
two sides proportionally. This is the Triangle
Proportionality Theorem. The converse is also true.
⃡ , then
⃡ ∥ 𝑅𝑆
If 𝑋𝑌
𝑋𝑇
=
𝑌𝑇
. If
𝑋𝑇
=
𝑌𝑇
⃡ .
⃡ ∥ 𝑅𝑆
, then 𝑋𝑌
̅̅̅, then ̅̅̅̅
̅̅̅̅ and ̅𝑆𝑇
If X and Y are the midpoints of 𝑅𝑇
𝑋𝑌 is a ____________ of the triangle. The Triangle
Midsegment Theorem states that a midsegment is parallel to the third side and is half its length.
1
⃡ and XY = RS
̅̅̅̅ is a midsegment, then 𝑋𝑌
⃡ ∥ 𝑅𝑆
If 𝑋𝑌
2
Example 1: In △ABC, ̅̅̅̅
𝑬𝑭 ∥ ̅̅̅̅
𝑪𝑩. Find x.
̅̅̅̅. Is 𝑯𝑲
̅̅̅̅̅ ∥ 𝑲𝑳
̅̅̅̅ ?
Example 2: In △GHJ, HK = 5, KG = 10, and JL is one-half the length of 𝑳𝑮
Guided Notes – SRT.4
̅̅̅̅ .
̅̅̅̅ and 𝐷𝐶
Example 3 – Find the lengths of 𝐵𝐷
Theorem
Pythagorean Theorem
The sum of the squares of the lengths of the legs (𝑎 and 𝑏) of a right triangle is equal to the square of
the length of the hypotenuse (𝑐).
𝑎2 + 𝑏 2 = 𝑐 2
Example 4 – Find the length of the altitude, 𝑥, of ∆𝐴𝐵𝐶.
Guided Notes – SRT.4
Example 5 – Find the unknown values in the figure using similar triangles.