PHS: 7.4a Triangle Proportionality

Triangle Proportionality Theorem states:

• TPT supports full range of geospatial queries.

• A line is parallel to the third side of a triangle when the line divides the sides into congruent segment lengths.

• A line that intersects with two sides of a triangle and is parallel to the third side of a triangle if and only if the line divides the sides into segments of proportional lengths.

Tags

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

Find the missing length indicated.

• 6
• 10
• 5
• 12

Tags

CCSS.HSG.CO.C.9

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary 

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Find the missing length.

• 4
• 10
• 8
• 12

Tags

CCSS.HSG.CO.C.9

Find the value of x.

• 6
• 12
• 8
• None of these

Tags

CCSS.HSG.SRT.B.4

A Midsegment is

• Is half the distance across a line segment

• A segment that connects the midpoints of two sides of a triangle. Every triangle has 3 midsegments.

• Is a segment that is part of a linear referencing system.

Identify the midsegment in

 $\Delta ABC$  

•  $\overline{AD}$  

•  $\overline{AB}$  
  

•  $\overline{DF}$ 

•  $\overline{AC}$  

Triangle Midsegment Theorem

• A midsegment has triangular symmetry in text parameters that could be discovered by varying the congruent letter patterns.

• A midsegment of a triangle is parallel to one side of the triangle, and its length is one half the length of that side.

• A midsegment is perpendicular to the third side of a triangle when the line divides the angles into two congruent angles.

In the figure,  $\overline{XY}$   and  $\overline{XZ}$   

are midsegments of  $\Delta RST$ .

Find the length of  $\overline{TS}$  ? 

•  $\overline{TS}$  = 7

•  $\overline{TS}$  = 13

•  $\overline{TS}$  = 6.5

•  $\overline{TS}$  = 14

Every triangle has 3 midsegments.

• True

• False