Triangle Inequalities § 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem

Slide2:

Segments, Angles, and Inequalities You will learn to apply inequalities to segment and angle
measures. 1) Inequality

Slide3:

Segments, Angles, and Inequalities The Comparison Property of Numbers is used to compare two line segments of unequal measures. The property states that given two unequal numbers a and b, either: a < b or a > b The same property is also used to compare angles of unequal measures.

Slide4:

Segments, Angles, and Inequalities The measure of J is greater than the measure of K. The statements TU > VW and J > K are called __________ because they contain the symbol < or >. inequalities a < b a = b a > b

Slide5:

Segments, Angles, and Inequalities SN DN 6 – (- 1) 6 – 2 7 4 > >

Slide6:

Segments, Angles, and Inequalities AB > AC AB > CB A similar theorem for comparing angle measures is stated below. This theorem is based on the Angle Addition Postulate.

Slide7:

Segments, Angles, and Inequalities A similar theorem for comparing angle measures is stated below. This theorem is based on the Angle Addition Postulate.

Slide8:

Segments, Angles, and Inequalities mBDA mCDA 45° 40° + 45° < < Use theorem 7 – 2 to solve the following problem. 45° 85°

Slide9:

Segments, Angles, and Inequalities For any numbers a, b, and c, 1) if a < b and b < c, then a < c. 2) if a > b and b > c, then a > c. if 5 < 8 and 8 < 9, then 5 < 9. if 7 > 6 and 6 > 3, then 7 > 3.

Slide10:

Segments, Angles, and Inequalities For any numbers a, b, and c, For any numbers a, b, and c, 1) if a < b, then a + c < b + c and a – c < b – c. 2) if a > b, then a + c > b + c and a – c > b – c. 1 < 3
1 + 5 < 3 + 5
6 < 8

Slide12:

Exterior Angle Theorem You will learn to identify exterior angles and remote interior
angles of a triangle and use the Exterior Angle Theorem. 1) Interior angle
2) Exterior angle
3) Remote interior angle

Slide13:

Exterior Angle Theorem In the triangle below, recall that 1, 2, and 3 are _______ angles of ΔPQR. interior Angle 4 is called an _______ angle of ΔPQR. exterior An exterior angle of a triangle is an angle that forms a _________ with one of
the angles of the triangle. linear pair In ΔPQR, 4 is an exterior angle at R because it forms a linear pair with 3. ____________________ of a triangle are the two angles that do not form
a linear pair with the exterior angle. Remote interior angles In ΔPQR, 1, and 2 are the remote interior angles with respect to 4.

Slide14:

Exterior Angle Theorem In the figure below, 2 and 3 are remote interior angles with respect to
what angle? 5

Exterior Angle Theorem 1 and 3 Name two angles in the triangle below that have measures less than 74°. acute

Slide19:

Exterior Angle Theorem

Slide20:

Exterior Angle Theorem The feather–shaped leaf is called a pinnatifid.
In the figure, does x = y? Explain. __ + 81 = 32 + 78 28 28° 109 = 110 No! x does not equal y

Slide22:

Inequalities Within a Triangle You will learn to identify the relationships between the _____
and _____ of a triangle. sides angles Nothing New!

Slide23:

Inequalities Within a Triangle in the same order LP < PM < ML mM < mP mL <

Slide24:

Inequalities Within a Triangle in the same order JK < KW < WJ mW < mK mJ <

Slide25:

Inequalities Within a Triangle greatest measure WY > XW 3 5 4 WY > XY

Slide26:

Inequalities Within a Triangle The longest side is So, the largest angle is The largest angle is So, the longest side is

Slide28:

Triangle Inequality Theorem You will learn to identify and use the Triangle Inequality Theorem. Nothing New!

Slide29:

Triangle Inequality Theorem greater a + b > c a + c > b b + c > a

Slide30:

Triangle Inequality Theorem Can 16, 10, and 5 be the measures of the sides of a triangle? No! 16 + 10 > 5 16 + 5 > 10

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: rfantster (46 month(s) ago)

The presentation is now (should be) downloadable.