ChapteChapter 4.2r 4.2

The Case of The Case of the Missing the Missing

DiagramDiagram

Objective: Objective: After After studying this section, studying this section, you will be able to you will be able to organizeorganize the the information information in, and in, and draw diagramsdraw diagrams for, for, problems presented problems presented in words.in words.

Set up a proof of the statement:“If two altitudes of a triangle are congruent, then the triangle is isosceles.”

1. Draw the shape, label everything.2. The “if” part of the statement is the

“given.”3. The “then” part of the statement is

the “prove.”4. Write the givens and what you want

to prove.

E

D C

B

A1. Draw a diagram to show two

altitudes in a triangle. Label everything.

2. Write your given statements.

3. Write your prove statement.

Given: BD & CE are altitudes to AC & AD of ACD.BD CE.

Prove: ACD is isosceles.

NOTICE!!!NOTICE!!!You can label everything on You can label everything on a diagram to help you a diagram to help you make the proof.make the proof.

Some problems you only have to draw, label, write the givens and what to prove.Others you also have to prove.

Remember If….then….Sometimes you will see these in reverse.

“The medians of a triangle are congruent if the triangle is equilateral.”

1. Draw the diagram.2. Write down the givens

you need.3. What do you need to

prove?

1. Draw a diagram to show the medians in an equilateral triangle. Label everything.

2. Write your given statements.

3. Write your prove statement.ZY

X

Q

RP

Given: XYZ is equilateral.PZ, RY, and QX are medians.

Prove: PZ RY QX

One more time. Try this one!“If each pair of opposite sides of a four-sided figure are congruent, then the segments joining opposite vertices bisect each other.”

1. Draw2. Write Given3. Write Prove4. Write proof

A B

CD

E

Given: AB CD AD BC

Prove: AC bisects BD BD bisects AC

Δ ABC Δ CDA by SSS, and thus, <BAC <DCA.

Δ BAD Δ DCB by SSS, and thus, <ABD <CDB.

Thus Δ ABE Δ CDE by ASA, and then AE EC and DE EB.