1) Create/make your own and unique story/word problem basing from your experiences, examples and videos you reviewed and explore.

2) Use your siblings/any member of the family or friends as the characters of the problem.

3) You will make or create ONE problem only.

ANY CONCEPTS AND SKILL FROM LESSON 7.4 - 7.5 - 7.6

7-5 Study Guide and Intervention

Parallel Lines and Proportional Parts

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.

If XY RS , then RX

XT

=

SY

YT

. If RX

XT

=

SY

YT

, then XY RS .

If X and Y are the midpoints of RT and ST, then XY is a midsegment of the triangle. The Triangle Midsegment Theorem

states that a midsegment is parallel to the third side and is half its length.

If XY is a midsegment, then XY RS and XY =

1

2

RS.

Example 1: In ABC, EF CB. Find x.

Since EF CB,

AF

FB

=

AE

EC

x + 22

x + 2

=

18

6

6x + 132 = 18x + 36

96 = 12x

8 = x

Example 2: In GHJ, HK = 5, KG = 10, and JL is

one-half the length of LG. Is HJ KL ?

Using the converse of the Triangle Proportionality

Theorem, show that

HK

KG

=

JL

LG

.

Let JL = x and LG = 2x.

HK

KG

=

5

10

=

1

2

JL

LG

=

x

2x

=

1

2

Since 1

2

=

1

2

, the sides are proportional and

HJ KL .

Exercises

ALGEBRA Find the value of x.

1. 2. 3.

4. 5. 6.

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 7 30 Glencoe Geometry

7-5 Study Guide and Intervention(continued)

Parallel Lines and Proportional Parts

Proportional Parts with Parallel Lines When

three or more parallel lines cut two transversals, they

separate the transversals into proportional parts. If the

ratio of the parts is 1, then the parallel lines separate

the transversals into congruent parts.

If l1 l2 l3, If l4 l5 l6 and

then a

b

=

c

d

.

u

v

= 1, then w

x

= 1

Example: Refer to lines l1, l2, and l3 above. If a = 3, b = 8, and c = 5, find d.

l1 l2 l3 so

3

8

=

5

d

. Then 3d = 40 and d = 131

3

7-6 Study Guide and Intervention

Parts of Similar Triangles

Special Segments of Similar Triangles When two triangles are similar, corresponding altitudes, angle bisectors, and

medians are proportional to the corresponding sides.

Example: In the figure, ABC XYZ, with angle bisectors as shown. Find x.

Since ABC XYZ, the measures of

the angle bisectors are proportional to

the measures of a pair of corresponding sides.

AB

XY

=

BD

YW

24

x

=

10

8

10x = 24(8)

10x = 192

x = 19.2

Exercises

Find x.

1. 2.

3. 4.

5. 6.

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 7 36 Glencoe

II. Rubric (Grading) for the Project Based Assessment.

(35 to 40 points)

- Creating a unique story/word problem that includes you, family members and friends as the characters of the problem.

- Appropriate content and skill are used for the problem. Student clearly internalize the mathematical concept applied to the problem.

- Showing all the the steps/work of the solution correctly.

- Proper language/mathematical terms are used and coherent "make sense" to follow and read.

(30 to 35 points)

- Not unique story/word problem. Avoid copying from your classmate(s).

- Appropriate mathematical content is not observed.

- Solution is incorrect and not showing all the steps/work.

- The word problem/story us not written in clear and coherent "make sense" to follow and read.

III. Modelling - Benchmark/Example:

FOLLOW THE STEPS IN YOUR TEXTBOOK ON PAGE 546, EXAMPLE 2- Real World Application

* Understand

* Plan

* Solve

* Check