how to connect external monitor for macbook air?
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['Connect a VGA display or projector: Use a USB-C VGA Multiport Adapter to connect the display to a Thunderbolt 3 (USB-C) port on your MacBook Air.', 'Connect an HDMI display or HDTV: Use a USB-C Digital AV Multiport Adapter to connect the HDMI display or HDTV to a Thunderbolt 3 (USB-C) port on your MacBook Air.']
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Make sure that your external display is turned on and connected to your Mac. Choose Apple menu  > System Preferences, click Displays, then click the Arrangement tab. Make sure that the Mirror Displays checkbox is selected.
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['Make sure that your external display is turned on and connected to your Mac.', 'Choose Apple menu \uf8ff > System Preferences, then click Displays.', 'Click the Arrangement tab.', "Make sure that the Mirror Displays checkbox isn't selected."]
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['Locate the Video Graphics Array (VGA) or Digital Video Interface (DVI) port on your laptop. ... ', "Plug the external monitor's cable into a VGA or DVI port. ... ", 'Locate an unused Universal Serial Bus (USB) port, which is identifiable as a small, rectangular hole on the side of your laptop.']
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The MacBook Air requires a mini DisplayPort to HDMI adapter. On an older MacBook Pro, you have two options: HDMI or Mini DisplayPort/Thunderbolt. As mentioned earlier, if your monitor has DVI, you can get Apple's Mini DisplayPort to DVI adapter. If your monitor has HDMI, you can plug an HDMI cable in directly.
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Apple Cinema and Apple Thunderbolt Display monitors are the easiest to connect, as MacBooks come build-in with ports that are compatible with any Apple monitor. All you'll need to do is connect the Mini DisplayPort or Thunderbolt cable attached to the display directly to your MacBook Pro.
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You need the following to use Target Display Mode: A Mac notebook or desktop with a Mini DisplayPort or Thunderbolt port. If your Mac has Thunderbolt 3 (USB-C) ports, you can connect it using the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter. A Thunderbolt cable or a Mini DisplayPort to Mini DisplayPort cable.
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['On your Mac, choose Apple menu > System Preferences, click Displays, then click Display. Open the Display pane for me.', 'Set both displays to the same resolution.', 'Click Arrangement, then select Mirror Displays.']
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You may be able to connect more than one display to your Mac. To do so, you need a video cable for each display. You might also need an adapter. After you connect the displays to your Mac, you can choose whether to use them as an extended desktop or for video mirroring.
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Choose the right cable and adapter. For the iMac, buy a Mini DisplayPort adapter that will enable you to connect the iMac to an external display. The adapter can be used for both Thunderbolt ports and DisplayPorts. This adapter allows you to connect your iMac to an external display via HDMI, DVI, or VGA.
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You can daisy-chain 2 Thunderbolt displays. You can also connect one mini DisplayPort monitor to the end of a Thunderbolt chain and connect your Mac to your Thunderbolt Display. A non-Thunderbolt solution if you don't have a Thunderbolt Mac: a DisplayLink-style USB to DVI display adapter.
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Connect the monitor cable from the second external monitor to the video port on the USB video adapter. If the connectors do not match, use the adapter plug that comes with the video adapter to match the connector on the monitor cable. Power on the second external monitor.
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['Insert the Mini DisplayPort plug on the adapter into the Mini DisplayPort or Thunderbolt port on your MacBook. ... ', 'Insert one end of the HDMI cable into the port on your adapter.']
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['Plug your Digital AV or VGA adapter into the charging port on the bottom of your iOS device.', 'Connect an HDMI or VGA cable to your adapter.', 'Connect the other end of your HDMI or VGA cable to your secondary display (TV, monitor, or projector).', 'Turn on your secondary display.']
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['Locate the "VGA" port on the side of the Compaq notebook. ... ', 'Insert the VGA cable into the port and screw down the pins on either side of the cable end.', 'Run the other end of the cable to the "VGA" port on the input panel of the external monitor.', 'Press the "F5," "F7" or "F8" key to enable the external monitor function.']
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['Turn off the HDMI device while your Mac is turned on.', 'Unplug the HDMI cable from your Mac, then plug it in again.', 'Turn on the HDMI device.']
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You could use one of the various DisplayLink products to connect one of your displays via USB and use a plain mini DisplayPort adapter for the other display (this would connect to your Thunderbolt port). Zotac provides an adapter to split a regular or mini DisplayPort into two HDMI ports.