Chapter 4 Part B

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Chapter 4 Part B

• By Britt, Anne, Emily, and Jacob

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Chapter 4.5 Notes

• Using Congruent Triangles
• GivenSDTC, CSDT
• Prove
• Plan for Proof Use CPCTC (corresponding parts of
  congruent Triangles are Congruent. By the
  Reflexive Property, STST. You can use the SSS
  congruence postulate to conclude that ?CST ?DTS
  Because of CPCTC, it follows

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CH. 4.5 Notes Cont.

• USING MORE THAN 1 PAIR OF TRIANGLES
• Given
• Prove

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4.5 Notes Cont
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4.5 Notes Cont.

• Proving a Construction
• Given HJ HG, GK JK

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4.5 Notes Cont.
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4.6 Notes

• Base Angles- Two angles Adjacent to the base.
• Vertex Angles- The angle Opposite of the base.

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4.6 Notes Cont.

• Theorem 4.6-Base Angles Theorem-If two sides of a
  triangle are congruent, then the angles opposite
  of them are Congruent.

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4.6 Notes Cont.

• Theorem 4.7- Converse of the Base Angles Theorem-
  If two angles of an opposite triangle are
  congruent, then the two sides opposite them are
  congruent.

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4.6 Notes Cont.

• Corollary to Theorem 4.6-If a triangle is
  Equilateral, then it is Equiangular.

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4.6 Notes Cont.

• Corollary to Theorem 4.7-If a triangle is
  Equiangular, then it is Equilateral.

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4.6 Notes Cont.

• Theorem 4.8- Hypotenuse-Leg (HL) Congruence
  Theorem-If the hypotenuse and a leg of a Right
  triangle are congruent to the hypotenuse and a
  leg of a second Right triangle, then the two
  triangles are congruent.

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4.7 Notes

• Coordinate Proof- is the placing of geometric
  figures in a coordinate plane.
• Using the Distance Formula
• A right triangle has legs of nine units and
  twelve units. Place the triangle in a coordinate
  plane. Label the coordinates of the vertices and
  find the length of they hypotenuse.

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4.7 Notes Cont.

• Solution- One possible placement is shown. Notice
  that one leg is vertical and the other leg is
  horizontal, which assures that the same vertical
  segments have the same slope, and the points on
  the same horizontal segment have the same slope.
  You can use the distance formula to find the
  length of the hypotenuse.

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Career In Geometry

• Hydrologist

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• Hydrologists study underground and surface water
  sources as well as the distribution and
  circulation of water in the atmosphere. These
  water sources include rivers, ponds, lakes,
  oceans, underground water supplies, and glaciers.
  The circulation of water in the atmosphere
  includes rain, snow, and other forms of
  precipitation.

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• Hydrologists commonly conduct research on climate
  assessment, erosion and sedimentation,
  hydroelectric power plants, irrigation systems,
  flood readiness, distribution and use of public
  water supplies, and the environmental impact of
  pollution on water quality. Hydrologists may be
  assigned to a specific project such as the
  development of an environmentally safe drainage
  plan for wastewater. Others may conduct research
  on a larger scale, aimed at developing new
  methods and techniques in hydrologic studies.
  Many hydrologists oversee a team of technologists
  and technicians.

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• Hydrologists may be considered under the general
  heading of Geologist. In addition to studying
  water, geologists concern themselves with soil,
  earthquake activity, hazardous waste sites,
  petroleum deposits, and other natural formations.
  A geologist's area of specialization defines his
  or her specific title. For example, petroleum
  geologists map the surface of Earth both
  underwater and on land for the existence of oil
  and natural gas. Mineralogists analyze, identify,
  and classify minerals according to their
  composition and structure.

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• Education and Training
• In the U.S., hydrologists may need the following
  education and training
• a bachelor's degree in environmental science,
  geology, or a related field for most entry-level
  positions
• a master's degree, or preferably a doctorate
  degree, in hydrology for positions in research or
  at a college or university
• On the Job
• Hydrologists often work with a team of
  scientists, technologists, and technicians. Much
  of their time is spent collecting data and
  performing experiments. This aspect of a
  hydrologist's work, called fieldwork, often
  requires extensive travel. The remainder of their
  time is spent analyzing data, drawing
  conclusions, and preparing technical reports.
• Math on the Job
• Most hydrologic studies require the ability to
  analyze data and draw conclusions. The
  information that hydrologists analyze is often
  numerical. For example, hydrologists may collect
  data on the movement and quantity of groundwater
  over time.

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Related Careers

• geologist
• geophysicist
• meteorologist
• mineralogist